- "F" stands for "Fuyumi (Asoh)" and "Fang (Gaia Memory in its in-series debut)"
- Part one's title is "Burglary Rider".
- Part two's title is "Reclaim your partner".
Whilst getting carried away again, this time with boxer training hell, Philip sees a dinosaur-shaped Memory that disappears as suddenly as it arrives. He tries to convince himself that it was just a hallucination, considering that it never really resurfaced after Begins Night, as well as what had happened when he'd last used it...
Meanwhile, the Detective Agency is visited by a bank teller Fuyumi Aso, who asks them to find a Kamen Rider. A ridiculously easy request—since she's unknowingly talking to one, right? ...Wrong. It turns out that the "Kamen Rider" she's talking about is but an impostor Dopant who has gone on a crime spree. After the Dopant robs an armored truck Shotaro arrives as Double to intercept him as the Dopant flees. Eventually, Shotaro and Akiko confront Fuyumi, because they suspect something fishy with her story, but they still need her cooperation. Fuyumi relents: she's one half of the Twin Rose cat burglar team. Kenji Kurata, the Arms Dopant, was the other half and Fuyumi's partner in crime.
Shotaro confronts Kurata, ordering him to discard the Arms Memory. Kurata refuses and transforms into the Arms Dopant, and fights Double until Kurata springs a trap. Akiko and Fuyumi are captured by Masquerade Dopants, and Arms threatens to kill Akiko if Double does not cancel his transformation. Though Shotaro intends to outwit Arms with Philip's help, Arms disables the right side of the Double Driver. Upon Arms revealing his target as Philip, Shotaro tells him to flee. With Masquerade Dopants on his tail, Philip runs into Saeko, the mastermind of the trap, whereupon she calls Philip Raito, the chosen child.
Philip then attempts to escape Saeko—whose Dopant form he recognizes as the commander from Begins Night—and encounters the Fang Memory again. Resisting its offer of power once more, Philip rides the RevolGarry, leaving Shotaro and Akiko behind. Kurata makes a call to him, demanding Philip's surrender in exchange for letting Shotaro live. While contemplating a way to rescue Shotaro and Akiko, Philip is visited by Watcherman, Santa-chan, and Makura, all looking for Shotaro. Philip also runs into Fuyumi, whose determination to get her partner back eggs him on.
Meanwhile, Shotaro and Akiko are caught in Kurata's sadistic trap, with Akiko's bleeding hands holding a rope preventing Shotaro from falling on spikes. Shotaro notes that the only way to escape is through the use of the Fang Memory, which weighed heavily on Philip's mind and body. The two are rescued by Philip and the Fang Memory, and the younger man transforms into Double FangJoker.
FangJoker fights in a berserk rage, overwhelming the Masquerade Dopants sent its way. Only the Arms Dopant stands in its way, and Double attacks Arms, almost slashing Akiko, just as Shotaro finds his partner within the burning Gaia Library. With Shotaro and Philip united, FangJoker is under control, avoiding Akiko. Double confronts Arms, defeating him with the newly named Fang Streiser Maximum Drive. Shotaro takes point and chases after Saeko as LunaTrigger.
Just as Double confronts Saeko as the Taboo Dopant, Kirihiko as Nazca saves her with his newfound speed. In the process Shotaro saves the reputation of Kamen Rider in front of Jinno by rescuing a girl.
As the case is closed, Shotaro wonders of things to come, as the Fang Memory encounters a blue beetle-like device...
Tropes within the arc include:
- The Berserker: FangJoker, at first.
- Big Damn Heroes: Philip and the Fang memory.
- Call-Back: To Begins Night in the form of FangJoker.
- Calling Your Attacks: Lampshaded by Shotaro naming the Finishing Move for FangJoker Fang Streiser.
- The Determinator: Akiko is forced to hold a rope that Shotaro was dangled on by the Arms Dopant. She continues even when exhausted and bleeding from her hands.
- Expy: Arms Dopant is clearly based on Jagi from Fist of the North Star.
- Mid-Season Upgrade: FangJoker
- Super Speed: Nazca first demonstrates it here.
- Wham Line: Saeko revealing Philip's real name.