On preserving dried ginger
Dried ginger can be kept at room temperature, in any cool dark place (like your pantry), for months to years:

Dried, ground, or crystallized ginger should be stored in a cool dark pantry in a sealed container. Spices with the moisture removed do not really go bad (unless they get wet), but they lose their potency over time and will no longer add flavor to food. If the aroma is gone, the flavor is most likely also gone from the dried ginger.

That's the whole point of drying it; so that it lasts longer without refrigeration.