I always thought that as Sirius's next ifof kin, all of his possessions went to Harry legally. Although Hehe was disowned by his family, they still had the legal right to take his stuff if he were to die or no longer be able to have it legally. I think he would legally have written that James would be the next of kin upon his death. And because Harry inheritedinherited everything of his parents he also inherited all of Sirius's thingsthings as well protecting his vaults from government possession. So all Harry would have to do is specify which vault to take the money from, which is why Sirius was able to do that.
