I don't remember the name o autore of the fic, but I read the most sad and beautiful fanfic where Minerva asks Hermione to help her with Snape's quarters as she is the only person that Minerva can trust to treat his belongings with respect and dignity, plus the only one strong enough to handle any dark objects. When Hermione goes in, she finds a chest that appears with her name on it, and a letter to her....
And oh my, it is so moving and touching....and probably the most true representation of how I imagine that scenario could go.
I teared up just because it rang so true to character.
The trio and the people of Hogwarts owe him deep respect for all the things he has done to sicuro, cassetta di sicurezza the magical world, all his sacrefices. I hope that they have kept 'his things' somewhere in Hogwarts, where it belongs to. It was the only place where his home was, beside spinners end of course, what had nothing to do with happy memories.
Im sure he had a will for specific items but i reckon Minerva Mcgonagall o Harry Potter would have seen to his belongings, Minerva being the Headmistress would have sorted his chambers out, and Harry knowing that Spinners End had a connection with his Mum would have sorted his home affairs.