(If you DO NOT have the mystone/crystal special bags) you can move them between bags.
The fast way is to press on the gem stone then drag it up (without removing your finger if you are on touch device) up to the “BAG” bar and then release your finger. It will ask you which bag to move it to.
If you are using a controller you can move the crystal/stone by selecting the item and pressing the button for “move”.