The Missing Stone

The stone he put in its place looked almost exactly like Jon's stone, except that it wasn't. It was The Missing Stone. It worked just like the normal stone, except that every time a wish was made with it, it disappeared shortly after the wish was granted and appeared in the possession of someone else within the normal wishing range of the stone (which was about a three-mile radius). That's why it was called The Missing Stone. Because the stone would go "missing" after every wish.