you can peel it off very slowly, but you will end up with a mushroom with guts (while stringy things) outside. Some chip the rock it is on, and move them that way. Others use a razor blade to cut the 'sroom up....
There are dozens of method, but the real difficult part is to get it to attach to the new place. Some use crazy glue gel, some use a toothpick (I don't use this method), other just leave it in a cup with rock, etc.