This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
You need to change this guy's heritage for good.
First, go to the Snail Stop, and buy some Jerky. Go back to 600 AD, and
give the Jerky to the lady in the elder's house. When she puts up an
offer to buy it, tell her you'll give it to her. She'll teach her kids
Now, go to the future, and the mayor will be willing to give you your
Moon Stone back.