"There is a popular theory that Crookshanks is actually Lily Potter's cat," the Quora post begins. "In The Deathly Hallows, when the trio are in Grimmauld Place, Harry reads a letter hand-written by Lily. In the letter, she mentions that they had a cat and that Harry almost ran over it with his toy broomstick. Harry even wonders if it survived the attack by Voldemort and if it was alive. In Prisoner of Azkaban, the owner at Magical Menagerie from where Hermione buys Crookshanks tell her that she had had Crookshanks for 'quite some time' and that nobody ever wanted him. This could correspond to our earlier timeline where the cat disappeared after Voldemort's attack on the Potters' residence. Soon after Crookshanks is bought by Hermione, he quickly recognizes Scabbers and the shaggy dog as Peter and Sirius respectively. The fan theory goes that Crookshanks recognized them both because they would have frequently visited Lily and James when he was with them."