Plus, it was her access to the time turner that allowed them to go back and save Harry, Buckbeak and Sirius to begin with.
That is until he and Hermione use her Time-Turner to save Hagrid’s condemned hippogriff Buckbeak and come across the aforementioned scene, waiting to see James Potter come to the rescue.
However, Hermione acknowledges that they are alone, helping Harry realize that it was he who conjured the Patronus saving him from the Dementors Kiss (or, in muggle’s terms, death by soul-sucking).
When Harry is able to save an injured Sirius Black (played by Gary Oldman in the film adaptation of Harry Potter and the Prisoner of Azkaban) with the assistance of a Patronus resembling a stag to ward off Dementors, the young wizard believes it was conjured by the spirit of his father.