For the Tormek stones and wheels, it is good idea to store them so that they are allowed to dry.

• The stones absorb water when in use : the SG and SB stones absorb quite a bit; the SJ stone less. In any regard, the stone will take quite a while to dry.
• The diamond stones don't absorb water, but water does get between the wheel and the back cover.

Note : When the stones are dry, there may be some discoloration. This is typically not mould; rather it is probably rust from embedded iron particles in the stone (from the last sharpening session). This is more particularly seen on the SG stone as that stone is lighter in colour.

The picture below from RickKrung is a great example of how to hang the stones. Hanging them vertically is recommended over laying them flat, though I can't give you a good reason why.

Storing grindstones vertically

The picture below from Ko Youngbin is a great example of how to store the stones horizontally. He uses a planting tray, with a mat to keep the stone above the tray's bottom.

Storing grindstones horizontally