This is what happens when a character tricks another character by writing a letter and signing it under a different name. Sometimes, the real writer's own handwriting was recognized, making the letter a big lie to the reader.
In more recent media, it may take the form of an e-mail or text message.
These can be used in a Batman Gambit, as they are usually written with the expectation that the recipient will react in a certain way. Quite often they can be used to lure someone into a trap. Other times they may be used to arrange meetings between people by a third party. They may also be used by well-meaning people to end a fight between others by sending a letter of apology on their behalf. How successful this can be varies.
WARNING: Unmarked spoilers ahead.
An episode of Maple Town dealt with the town mayor, Dandy Lion, making himself sick over not getting an answer from a letter he sent to his estranged daughter. Patty Rabbit and her big sister, Rachel, write their own letter (writing it as if the mayor's daughter sent it) and send it to Mayor Lion in order to make him feel better.
Pokémon episode "Wherefore Art Thou, Pokemon?". Two young Trainers, Emily and Ralph, hate each other even though the Nidorans they own are in love with each other. Misty schemes to write Emily and Ralph each a letter supposedly from each other so that they will fall in love too.
W.I.T.C.H.: When Matt gets sucked into a magic book, leaving the girls to try and cover up his disappearance, which includes writing an e-mail to a friend using his e-mail account, which they gained access to by guessing that his password was Will's name. Peter, the one they send it to, realizes something is off, since usually Matt's e-mails are full of typos, and this one, written by Cornelia, was not.
In Sunset Boulevard, the fan letters that Norma had been getting over the years were actually written by her butler Max to spare her from the fact that the public had forgotten her.
In Red Riding Hood, Valerie's sister is tricked outside at night by the wolf when he forges a letter from the boy she's in love with.
The Four Musketeers (1974). Milady send d'Artagnan a case of poisoned wine along with a letter supposedly from Athos, Porthos and Aramis. Luckily d'Artagnan decides to find them first before drinking the wine.
Out of everything else that Tony, the monstrous pimp from Thriller: A Cruel Picture, did to Madeline (including putting out one of her eyes for refusing a client), by far his most despicable act was to forge a letter to her parents in her name, telling them that she hated them and not to bother trying to find her. When Madeline seeks out her parents after escaping him, she learns that the letter had the effect of driving them to suicide. This is the final straw that sets the stage for one hell of a Roaring Rampage of Revenge.
In Amélie, one of Amelie's neighbor is bitter that her husband left her for another woman, then died in a plane crash. So Amelie creates a fake letter to convince the neighbor that the husband wanted to reconcile with her, had left his mistress, and was on his way home when the plane crashed.
In Neighbors 2014, the protagonists live next to a frat house which is one strike away from being expelled from their college. The protagonists wait for the fraternity to cause more trouble so they can report them, but they refuse to have any additional parties. The protagonists forge a letter from their college convincing them they are off probation, causing the fraternity to receive a third strike.
Mulan: Mushu gets Mulan's force into the war by having Cri-kee write a fake letter from the general urgently ordering the new recruits into action.
In the book of Ella Enchanted, Ella realises that if she were to marry Char, her curse would make his life difficult and even dangerous. So she writes a letter in her own handwriting, claiming she's run away with a rich lord, then writes an accompanying letter in her stepsister's handwriting, terrible spelling and all, to back it up. It doesn't work. He just thinks the letter from her is fake, instead.
Heralds of Valdemar series. In [Brightly Burning, a forged letter is used to lure Lavan out where the assassins can get a shot at him.
In And Then There Were None, the culprit sent a letters to all his victims under different names, to trick them into comming to Soldier Island. And going by the first scene of the book, the culprit also sent a fake letter to himself... for some reason...
In Terry Pratchett's Going Postal, con-man Moist von Lipwig secures an immediate reservation for himself and his girlfriend at the poshest and most expensive restaurant in Ankh-Morpork by forging a letter from financier Reacher Gilt. Gilt, a master con-man himself, recognises a worthy opponent by graciously offering to pay their bill...
On Don't Trust the B---- in Apartment 23, James gets a letter each year from his Dawson's Creek castmates inviting him for a reunion show, which he always rejects. Turns out the letters were actually from Chloe, which she uses as an excuse to get James to do whatever she wanted to cheer him up.
In Bottom, Richie receives birthday cards from himself every year - only he claims they are from grateful Soviet citizens, Sue Carpenter and the crew of the Ark Royal. Eddie barely manages to play along with the joke with his usual dripping sarcasm:
Eddie: ...and this one's from "The people of the Soviet Union, in grateful thanks to Comrade Richie."
Happens on House of Anubis- Eddie, with KT's help, forged a break-up letter for Fabian claiming it was written by Nina. Fabian didn't fall for it, however, because he knew that the letter was written in a way Nina didn't write. Eddie didn't do it to be malicious; He DID have a letter from Nina for Fabian, but lost it, so tried to make his own instead.
Carla is upset because her husband Eddie is out of town and didn't remember Valentine's Day, so the guys all pitch in to buy her a flower delivery. She catches on when she sees that the card is signed "Eddie," which isn't her husband's real name.
In the Ballet Episode Sam forges a letter from the Boston Ballet saying that Diane would've be a perfect fit for their company 10 years ago (which in context should be perfectly acceptable to Diane, since she knows she's "over the hill" to become a ballet dancer). But then she decides to try out anyway and is terrible.
Leverage: After the team foils an attempt on the life of a client in "The Homecoming Job", they find a suicide note on the hitmen intended to make it looks like he'd been Driven to Suicide.
M*A*S*H. Klinger occasionally would forge letters, particularly in mail call episodes, in further attempts to get a discharge; Henry kept many of Klinger's letters on record and uses them against him to point out how ridiculous the claims in the letters are, leading up to one letter that reads, "Half of the family dying, other half pregnant." Potter, on the other hand, dug a little deeper when Klinger tried to pull a similar stunt on him. Incidentally, Klinger has no brothers.
Potter: Klinger, this letter is in your handwriting.
Klinger: I translated my mother's letter, it was in Lebanese.
Potter: Let me see it.
Klinger: I burned it.
Klinger: It's part of a religious ceremony.
Potter: Held when two brothers die in a harmonica factory?
Call of Cthulhu campaign Shadows of Yog-Sothoth, adventure "The Coven of Cannich". After the witches (Cthulhu Mythos cultists) in Scotland kill Henry Hancock, they send a fake letter supposedly written by him to his nephew Jacob to cover up his death.
In the Professor Layton game Professor Layton and the Lost Future (or Unwound Future), Clive pretends to be Luke from 10 years into the future, he writes a letter dated ten years into the future requesting the esteemed Professor's help and signing it as his apprentice, including an address which contains a lift to below the tube, where the 'future' has been built and Clive attempts to get revenge on Professor Layton by pretending to be the boy closest to him. There is an actual time machine though.
In Team Fortress 2, sending a "tear stained letter" each to both his brothers is how Grey Mann convinced his two brothers to meet and reconcile so he could kill them both.
Anaksha Female Assassin. In the Mini-Adventure "Quick Stop," Anaksha does this to save the job of a convenience store clerk who did her a good turn by allowing her to use the store's restroom, which is normally reserved for employees only, but was ratted out by her rather crankish co-worker. The document in question is a letter of apology, which some unscrupulous employers use as a trick to get a signed confession out of someone so they can have a legal excuse to fire the person anyway, denying them any grounds for a lawsuit. Anaksha does this to allow the clerk an "out" in this should they indeed decide to fire her, and offers her a job at the Zaranna Corporation in case all else fails.
There is an early quest in Skyrim that involves giving a fake letter from Faendal (actually written by Sven) and giving it to a girl they both like. The player can then choose to tell Faendal about the letter, and can choose to deliver a similar letter from Sven (actually written by Faendal).
In Plants vs. Zombies, the Zombies at one point send you (the home owner) a forged letter claiming to be your mother inviting you over for meatloaf, asking you to leave your front door open and your lawn unguarded. It is signed as "mom (not the zombies)".
In the Thieves Guild questline in Oblivion, the player is tasked to forge a letter of recommendation, in order to get rid of the troublesome Watch Captain.
An unintentional variation happened in Final Fantasy IX. The local Genki Girl wrote a love letter to the protagonist, but forgot to sign her name. After a series of wacky hijinks when the letter got to unintended addressees and was thought as originating from various people, it brought the Beta Couple together. Accidentally.
A major plot point in chapter 3 of The Witcher, where Thaler suspects that someone is forging the absent King Foltest's letters. He is right.
In Grand Theft Auto V, Trevor has been keeping contact with Bradley via email while the latter is in prison for their botched heist. It's later revealed that Bradley died in the shootout following the heist and the guy he's actually been emailing is FBI agent David.
A plot point of Gyakuten Kenji 2 involves a hidden mastermind manipulating individuals by typing letters signed as other people, predicting that a few key words would push them to act as the mastermind wanted.
In one of the Three Little Pigs shorts, the Wolf captures two of the pigs and writes a letter to Practical Pig pretending to be from his brothers in an attempt to lure him out. Practical doesn't fall for it: along with the bad penmanship, he recognizes the Wolf's breath when he blows it under the door.
Avatar: The Last Airbender: Sokka attempts to pull this in "The Runaway" episode, in order to patch things up between his sister Katara, and their friend, Toph. So he writes a fake apology letter and sends it to Katara, via messenger hawk. It fails hilariously, after she reads it and points out a rather obvious oversight in her brother's plan:
Katara: (shouts, while pointing at fake apology letter) "I know this is from YOU, Sokka! TOPHCAN'T WRITE!!"
In an episode of The Simpsons Bart creates a boyfriend for his teacher Mrs Krabappel and writes her letters based on his parents' old loveletters, pretending to be a guy called "Woodrow".
In one episode of TaleSpin one of Shere Khan's executives, Benson, tried to force Louie out of his club by writing a letter that said, "Do whatever Mr. Benson says." and forging Khan's signature, thus making the Khan pilot force think they were on a sanctioned assignment.
A variant of this happens in SpongeBob SquarePants episode "Naughty Nautical Neighbors", in which Spongebob and Patrick, at their homes, communicates via speeches in soap bubbles. The noises disturb Squidward (whose house are between the two's) who's eating a cake at the moment. Frustrated, Squidward shakes his fork on the plate, at which point it creates foams (presumably from the cake). Squidward then gets an idea of stopping them: "sap" the communication line by stopping their bubbles mid-flight, and then using his own foam to create speech soap bubbles that are filled with unsavory messages for Spongebob and Patrick (who are unaware that Squidward did it). This drives the two to hate each other for the remainder of the episode. Fridge Logic comes when Squidward's soap bubbles looked different from the normal one, and it's also filled with Squidward's voice and yet they don't recognize the voice.
In an episode of The Looney Tunes Show, Daffy and Porky get into a feud over who ordered the french fries at Pizzaribba. Bugs wants them to make up with each other so he can go to a football game that Porky has the tickets for, so he sends each of them a gift basket and an apology card with each other's names. At first, this seems to work, but then they get back to arguing with each other. When Bugs flat-out admits he wrote the cards and that he doesn't care about their feud and just wants to see the game, Porky snaps and rips up the tickets so none of them can go.
The ending to the Very Special Episode has Quagmire kill his sister's abusive boyfriend and he and the guys go to her with a fake letter telling her that "he" is leaving her, that he will kill her and her unborn child if she tells that he was with the guys, and that he really, really likesGrape Ape.
Quagmire: I should have known that Cheryl Tiegs didn't write me that letter. She would have known there's no "a" in the word "definite".
The Arthur episode "The Big Blow-Up" concerned Francine and the Brain getting into an argument with each other, which puts a damper on a soccer game that they, along with Arthur and Buster, were partaking in. On the day of the big game, Arthur and Buster both forge fake apology letters to Francine and the Brain, with Buster writing the Brain's apology letter to Francine, and Arthur writing Francine's apology letter to the Brain.
Recess. In "Omega Kids," T.J. and the gang are the only ones attending school for a number of days after the rest of the students fall ill from eating tuna fish tacos, which slowly starts to drive them crazy, to the point that Gus tries to pull a stunt by handing Miss Grotke a note, which T.J. snatches from him and reads for himself.
T.J.: (Reading the note) "Dear Miss Grotke, please our son Gus from school, he is so sick he should probably stay home until all the other kids are better. Signed, 'My Mom' "?
Vince: That's pathetic.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
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You are saying this draft has a ready-to-publish hat it does not deserve and you are taking it back.