Harry is the one who brought up the Resurrection Stone with the assumption that it behaved like other devices, in the aptly named chapter, "Pretending to be Wise, Pt 2". The Defense Professor is the one who reacted as if shocked to the news that - if his genealogy search went the way Voldemort's did in canon - he already had the artifact:

Harry said hastily, "I did think fast enough not to suggest the obvious idea about the Resurrection Stone in front of Dumbledore. Have you ever seen a stone with a line, inside a circle, inside a triangle?"

The deathly chill seemed to draw back, fold into itself, as the ordinary Professor Quirrell returned. "Not that I can recall," Professor Quirrell said after a while, a thoughtful frown on his face. "That is the Resurrection Stone?"

Harry set aside his teacup, then drew on his saucer the symbol he had seen on the inside of his cloak. And before Harry could take out his own wand to cast the Hover Charm, the saucer went floating obligingly across the table toward Professor Quirrell. Harry really wanted to learn that wandless stuff, but that, apparently, was far above his current curriculum.

Professor Quirrell studied Harry's tea-saucer for a moment, then shook his head; and a moment later, the saucer went floating back to Harry.

Harry put his teacup back on the saucer, noting absently as he did so that the symbol he'd drawn had vanished. "If you happen to see a stone with that symbol," said Harry, "and it does talk to the afterlife, do let me know. I have a few questions for Merlin or anyone who was around in Atlantis."

"Quite," said Professor Quirrell. Then the Defense Professor lifted up his teacup again, and tipped it back as though to finish the last of what was there. "By the way, Mr. Potter, I fear we shall have to cut short today's visit to Diagon Alley. I was hoping it would - but never mind. Let it stand that there is something else I must do this afternoon."