Getting somebody reading a whole letter out loud in fiction is plain boring. So, at sometimes you'll notice that their voice fades and gives way to the sender, even though that's in a different room/town/timezone, before fading back to the reciever at the end. Bonus points if the letter is read while we see where the sender is, or where s/he was while writing the letter.
Often combined with Dead Man Writing for a Tear Jerker—or at least an attempt at one. More comedic shows may do a Left the Background Music On style gag: Bob sits reading his letter, while we hear someone reading the message, only for Bob to turn round and ask if he can read his letter in peace, please.
See also Epistolary Novel, Sounding It Out.
Examples:
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Anime and Manga
There's a case from Yu-Gi-Oh! when Tea reads Pegasus's diary.
Kiki's Delivery Service, the letter right near the end. Her father begins reading it but it fades out into Kiki's voice.
When Cobra gets Vivi's letter in One Piece, which reveals Crocodile to be the mastermind behind the Alabasta civil war, she begins reading the letter aloud.
In Bleach, Aizen's letter to Momo, which he leaves behind just before his apparent death, is read aloud in his voice.
All the time in You've Got Mail. In her commentary Nora Ephron made it clear that she wanted to get away from the computer screens ASAP, for fear that the audience would get spooked and leave the theater.
Played with in Harry Potter and the Goblet of Fire. Harry reads an article by Rita Skeeter, and we hear her voiceover of what it says. A few sentences in, it pisses him off so much he throws it into the fire, and Rita's voice first tries to cram in as much as possible, and then screams as the article burns.
Inverted in Top Secret!. Nick Rivers arrives at his banquet table and finds a note. As he starts reading it, the agent's voice appears, slightly distorted. Then, as Nick appears to finish the note, the agent appears, talking in stride with the letter with a small megaphone over his mouth.
Subtly played with in Back to the Future Part III. At the end of Part II, Marty receives a letter from the late, time-displaced Doc Brown which had been sent 70 years prior. Marty begins to read it aloud... and then the next morning it's read aloud for both Marty and the audience by Doc Brown's younger self.
Live Action TV
Occurs whenever Lizzie reads a letter in the BBC production of Pride and Prejudice.
Baywatch episode "Baywatch Down Under Part 2". As Jake reads a letter from his ex-wife Clare, we first hear it in his voice, then hers. Bonus points because she's deceased at the time.
On CSI: Crime Scene Investigation, when Sara leaves, v. unexpectedly, the letter is read in her voice, with shots of her in a taxi, as Grissom reads it. Major Tear Jerker.
Spoofed in an episode of Scrubs where it initially looks like an example of this trope, Dr. Cox sitting reading a letter from J.D. with J.D.'s voiceover, but then the camera zooms out to show J.D. is in fact, right there, reading the letter he wrote out loud over Dr. Cox's shoulder.
Lampshaded in the sketch show Exit 57, where Amy Sedaris's voiceover gave way to a hacking smoker's cough during the first sentence of her letter, forcing her to start over.
Parodied in My Hero: Cassie runs away, leaving a letter for her parents. At first, the trope seems to be upheld, then Janet asks George to stop reading it out loud in Cassie's voice.
Manhua
At the end of Infinity Gamethis is subverted. It looks like Long Wei is reading out his letter to Lu Xiao, but really he's writing his diary as though it were a letter to her and she's reading a menu somewhere else.
Radio
Spoofed all over the place in Bleak Expectations. It often happens with Mr. Benevolent's letters in particular, where Benevolent's voice reads the letter ... then the character actually reading aloud is complimented on how well they can do the voice.
Theatre
Used in The Musical of The Phantom of the Opera, with a letter starting to be read by one of the managers, but then it switches to the Phantom, before ending with the manager again. In The Movie of the The Musical, we see the Phantom illustrating what he's talking about in the letter with a diorama.
In Tales Of Symphonia, Collete's voice is used as the voiceover when Lloyd reads a letter from her.
In Tales Of The Abyss, Luke, after being separated from his friends for around a month late in the game, reads letters from Tear, Anise and Guy, and their voices describe what's been going on in their lives.
In Eternal Darkness, one of Edward's later letters to his granddaughter Alexandra, regarding how she can defeat the Ancient that Pious is summoning, is read aloud in his voice, and this is the only letter in the game that receives this treatment, emphasizing its importance.
Oni has Konoko reading her father's memoirs like this. Specifically, the part that narrates how he met his wife and how he took her life via Mercy Kill.
In a Rooster Teeth short, Kerry the intern is ordered by Gus to mow the lawn on the company campus with a push mower (When Kerry asks why he can't use a motorized mower like normal people have since thier invention, Gus yells at him about the price of gas before walking away). As Kerry attempts to mow, he stumbles across a box labeled "Gus' Time Caspule" or something along those lines. He finds some random things inside including a letter, which he begins to read. The letter is read and narrated in Gus' voice, getting progressively creepier and stalkerlike towards Kerry until at the end, where Gus is shown to be reading the letter out loud over Kerry's shoulder with his shirt off.
Spoofed in the animated Aladdin TV series. The letter from Genie is being "read" in his voice, but then we cut to the other side of the shot and see that the letter is actually a mouth reading out loud.
Happens twice in Beforel Orel: First, Orel writes a letter to his grandfather, revealing that he plans on murdering his baby brother. At the end, Grandpa writes a letter to Orel telling him that he's a good child and not to let growing up in Moralton affect him.