After giving the item to Klein, it's never explained what became of the item. The reason for this is because of the way SAO was written. I would go into details, but I'll try to make it simple.
SAO was originally a Web Novel, written from 2002 to 2008, before the author was asked to publish it in 2009. Most of the side-stories that took place in the "Aincrad Arc", were written around 2002-2004 (After the first "Volume" was already written), between the other major arc, Fairy Dance and Phantom Bullet. "Red Nosed-Reindeer" (the story that Episode 3 is adapted from) is different. Kawahara didn't write this story until after 2005, when he had already began writing the final arc of SAO (which isn't even in the anime yet)
Effectively, when he first wrote SAO, the Stone was not a concept he had in mind. When he began publishing, he never bothered to write the stone into any other story either (even though he included "Red-Nosed Reindeer" as a side-story in the second book)
I would have to assume that the stone was used to save one of Klein's Guildmates, considering that in the novel it was said that his Guild never suffered a single casualty.