From what I could gather with the information in the pokedex, females of the species can evolve with use of the stone into something called a Frostlass. Otherwise they simply evolve into a Glalie when they are strong enough as the males do.

[He's only been here like a week, but if he's going to gain power in this world he will need strong pokemon. That means research on what he has!]

Snjokorn seemed excited when I brought up the prospect. [There's that too.]