Harry and Hermione travel three hours into the past, watching themselves move through previous events. They realise that Dumbledore wanted them to travel three hours back to not only save Buckbeak from being wrongfully executed, but also to use Buckbeak to free Black from West Tower. After narrowly rescuing Buckbeak at the right moment before Macnair can execute him (so Dumbledore and Hagrid would not be accused of setting Buckbeak free), Harry and Hermione hide near the Whomping Willow in the Forbidden Forest to wait for the "other Harry and Hermione" and everyone else to return from the Shrieking Shack. During this time, Harry tells Hermione about the man he saw across the lake and how he thinks it was his father who conjured the Patronus.
After two hours, following Lupin's transformation, Harry decides they need to head back to Hagrid's empty cabin so Lupin doesn't attack them. After spending some time in hiding, Harry leaves the cabin to check out the present situation and sees himself, Hermione, and Black fainting from Dementors. He realises that the silver stag he saw earlier across the lake was not cast by his dad and conjures a powerful Patronus that drives all the Dementors away. When it returns to him, he pets it and realises that it was the same Patronus as "Prongs," his father.
After Hermione and Buckbeak catch up, they wait until they see Macnair leave the castle to retrieve the Dementors. He and Hermione then fly Buckbeak up to West Tower and rescue Black. Harry and Sirius say their goodbyes before Sirius flies away on Buckbeak.