Unlike many other mushrooms, puffballs can be frozen raw, then thawed for cooking and will not suffer from it. After freezing to "cook" them, I remove the water, vacuum seal and re-freeze.
Fresh puffball mushrooms, firm and white throughout
Instructions
Clean the mushrooms
Trim the base where the puffball mushrooms were attached to the ground, carving out any portions damaged by bugs. The puffballs should be pure white and firm inside.
"Freeze cooking"
Put the puffballs whole, skin-on in the freezer, of, if you don't have that much space, cut them into large pieces or quarters.
Thawing
Allow the mushrooms to thaw at room temperature on a tray with sides to catch the water that will release.
Compress and remove water
Peel the skin from the puffballs, you will find this is much easier than doing it fresh, and it will often peel off in a single piece.
Cut the puffballs into 1 inch or thinner slices, using a long sharp knife.
Put the slices of puffball between a couple layers of paper towel, then press a rolling pin over them. A good amount water will be released.
Take the compressed slices of puffball and put them in a vacuum seal bag with a folded paper towel at the top of the bag as flush with the sides of the bag as possible to prevent any excess liquid from getting into the vacuum sealer. Seal the puffballs, label, date, and freeze until needed.
Cooking
To cook the puffballs from frozen, simply thaw them, remove from the vacuum bag, and cook as you would fresh.