Answer first: dry, cold, dark and still, with the lot code where you can still read it in a year.
Lyophilised powder: refrigerated at two to eight degrees for months, frozen at minus twenty for longer. The gain from minus eighty over minus twenty is small for a dry solid and is not usually worth the arrangement.
Reconstituted with a preservative-containing diluent: refrigerated, conventionally treated as usable for about 28 days from first entry. Without a preservative, single use and discard.
Photodegradation of tryptophan-containing peptides is documented and is the basis for light-protected storage recommendations.
Nothing here is medical advice, and research-use compounds are not approved for human use.
Equilibrate before opening or you condense water into the cake.