I like to save intact skins too, for when I share my snakes with the public for "meet & greets"; skins & eggs are great props that help people to learn more about them.
Sometimes a snake will defecate right into their shed as they "undress"- keeps the cage neat but that shed is a total loss for saving, lol...
As Sonny1318 said, the time to work with (unroll) the shed skin is while they're damp, and one thing that makes it easier to dry them flat is to blow into the mouth
part of the shed (don't actually touch it with your mouth) to inflate the skin, then lay it flat to dry.
Shed skins will last a long time, as Zincubus said, UNLESS you live some place where the wrong moths get a hold of them. Be aware that certain types of
moths will EAT them, so if you save them, keep them in a tight container.