Here's the breakdown:
* He initially retrieved it: Harry found the stone in the Chamber of Secrets, after defeating Voldemort's plans to steal it.
* He didn't keep it: He gave the stone back to Dumbledore, who decided it was too dangerous to keep in the school.
* The stone was destroyed: Dumbledore destroyed the stone to ensure it couldn't be used for evil purposes.
So, Harry did possess the stone, but only for a short time. He didn't keep it, and it was ultimately destroyed.