Harry and Hermione fly up to Flitwick's office, rescue Sirius on Buckbeak's back, and Sirius takes off with a fond farewell.

Time Travel
Harry and Hermione sneak through the woods over near the Whomping Willow, to watch the scene unfold. They watch themselves disappear underneath the tree and then watch as Lupin, Hagrid, and Snape pass as well.
While waiting for themselves to re-emerge from the Whomping Willow, Harry tells Hermione about the [Patronus] that drove the [dementors] away - and that he thinks he saw being cast by his father.
Expecto Patronum!
As they watch themselves reappear from the Whomping Willow, Harry and Hermione realize they must get out of the way of the oncoming werewolf, and take off for Hagrid's hut. There Harry decides to set off to watch the scene unfold, and departs alone.
Harry rushes over by the lake, watching the [dementors], and runs to see who cast the [Patronus]. After a moment, though, he realizes that he hadn't seen his father, but himself. He casts the Patronus, and just has time to see that it's a stag before it vanishes.
Hermione returns and drags Harry into hiding once more, where he tells her about the [Patronus], they watch Snape take themselves and [Sirius up to the castle], and they see [Macnair] pass by with a [dementor], making them realize it's finally time to rescue Sirius.
Chapter 22 - "Owl Post Again" - In which Harry and Hermione safely return to the hospital wing, where Snape arrives to blame them for Black's escape but cannot prove it. Lupin resigns, returning the invisibility cloak and Marauder's Map to Harry. Term ends, HRH return home on the Hogwarts Express, Harry gets owl post from Black, and Ron gets a new owl.
Meanwhile, Back in the Hospital Wing...
With Sirius Black gone, Harry and Hermione realize they have only ten minutes to get back to the hospital wing, and after hiding from Fudge and Snape and then Peeves, they only just make it in time for [Dumbledore] to lock them inside.
Madam Pomfrey comes in to give Harry and Hermione [chocolate], but they're interrupted by an irate Snape, accompanied by Fudge and [Dumbledore]. Snape tries to blame Harry for Sirius Black's escape but has no luck, and finally storms off. Once Fudge and Dumbledore leave, Ron awakens, and Hermione begins to explain all that's happened.
Exit Professor Lupin