Store stamps with their caps attached.
Also, note that stamp grips are made of wood, so you should observe the points below.

Moisture
Grips are prone to damage by moisture and humidity. Droplets on a grip can permeate the wood,
even if wiped off immediately, causing the trip to swell. Moisture can also cause mold and mildew to form on a grip.

Storage
Do not store grips in a location exposed to direct sunlight, or subjected to high temperatures or humidity.
Such conditions can cause cracking and the formation of mold and mildew.