The case of Buckbeak is quite complicated because its ownership was not officially transfered. At the beginning of "Prisoner of Azkaban" it belonged to Hogwarts. At the end of a school year it was stolen by Harry and Hermione and given to Sirius who then possessed Buckbeak for the next two years. This was encouraged by Dumbledore the Headmaster of Hogwarts, because of two reasons:
- Buckbeak would be executed by Ministry of Magic if it stayed at Hogwarts,
- Dumbledore wanted to help Sirius escape the castle.
So we can tell that de iure Buckbeak still belonged to Hogwarts as a lost property, but de facto it belonged to Sirius, as Dumbledore secretly gave the animal to him.
Later, at the beginning of "Half Blood Prince" Dumbledore tells Harry:
Sirius’s will was discovered a week ago and that he left you everything he owned.
As no special clauses are mentioned we can assume that Sirius's will contained only this one sentence. As Buckbeak was at Sirius's house and he had been taking care of it, someone else must take the hippogriff. Dumbledore said that now it belonged to Harry:
There is also the matter of the hippogriff, Buckbeak. Hagrid has been looking after him since Sirius died, but Buckbeak is yours now, so if you would prefer to make different arrangements —”
With this sentence Dumbledore confirmed his previous (not explicit) will that Buckbeak belonged to Sirius. He also proposes that the school reclaims the hippogriff but with a different name, so the ownership issue is closed and Buckbeak belongs both de facto and de iure to Hogwarts, but using a different name (Witherwings) and pretending it is another animal. As Harry accepts this offer, the issue of ownership is solved by gentleman's agreement between two people who might claim it: Harry (inheritor of Sirius) and Dumbledore (Headmaster of Hogwarts).