Chapter 18 - "Moony, Wormtail, Padfoot, and Prongs" - In which Lupin tells the story of his becoming a werewolf and of his school days with James Potter, Sirius Black, and Severus Snape, the last of whom now appears.

Lupin Tries to Explain
Unexpectedly, Harry, Ron, and Hermione discover that Lupin is siding with Sirius Black, outraging Harry and Hermione again. But when they accuse him of treachery, he returns their wands, and asks for a chance to explain.
Given a chance to calmly explain, Lupin tells Harry, Ron, and Hermione how he had been watching the Marauder's Mapand discovered that [Peter Petigrew] is still alive and has been living as Scabbers.
Harry, Ron, and Hermione all belive that Lupin and Sirius are crazy to believe that Scabbers is Peter Pettigrew. Black lunges for Scabbers but Lupin insists that Harry, Ron, and Hermione have a right to know the truth.
Unregistered Animagi
Harry insists that there were witnesses to Pettigrew's death while Hermione insists that Pettigrew can't be an Animagus because he isn't on the register. Lupin explains how he was bitten as a child, how his friends discovered the truth of his transformations at school, and how Sirius, James, and Pettigrew became unregistered Animagi to keep him company during Lupin's transformations.
Lupin expresses his guilt at betraying Dumbledore's trust by not telling Dumbledore that Sirius is an unregistered Animagus. Lupin feels as though Snape might be justified in his distrust of Lupin. Sirius is interested to learn that Snape is a teacher at Hogwarts.
Lupin and Sirius explain how they were classmates of Snape's and how much Sirius, James, and Snape hated each other. Lupin relates the story of the near-fatal joke that Sirius played on Snape. While all are talking, Snape emerges from under the Invisibility Cloak, his wand pointed at Sirius.
Chapter 19 - "The Servant of Lord Voldemort" - In which Snape threatens Lupin and Black with the Dementors, HRH disarm Snape with a spell, Lupin and Black tell the truth about Harry's parents' deaths, Scabbers reverts back to Peter Pettigrew, the truth comes out about all the players in the drama, revealing that Pettigrew was responsible for the Potters' deaths, and Harry keeps Lupin and Black from killing Pettigrew.
Wormtail is Caught Like a Rat in a Trap
Snape refuses to listen to the protests of Sirius, Lupin, or the kids, and instead is determined to see Sirius and Lupin fed to the [dementors] - until he makes Harry, Ron, and Hermione so angry that they all [disarm] him at once, knocking him out.
With Snape knocked out, Sirius and Lupin continue explaining the background behind Peter Pettigrew, and finally force Peter to reveal himself and confront him with the things he did. But when they try to kill him, Harry stops them - and they agree to bring him back to the castle instead.