Collectible Drinking Glasses

My mother has a lot of glasses collection, she bought 20 years ago. Any ideas on how to safely store them. Currently they are just in the box between each other.
We'll start orgainizing all his business and moving it in a shed of ours and trying to get rid of cardboard boxes that are deteriorating.
And good storage solutions?

Store in freezer and Thata when someone needs a cold drink, the glass will freeze.

The lenses are safer in boxes that separate them. Why not buy plastic storage bins large enough to put all the boxes inside. There are other ways to store and does not take much space, but you said they are collectibles. You must decide how precious they are and the degree of security you want to keep.