Start with the physical state, because lyophilised and reconstituted material have completely different storage answers.
Let a refrigerated or frozen vial equilibrate to room temperature before opening, so humid air does not condense water onto a cold cake.
Keep the certificate with the vial, physically or as a photograph filed under the lot code. A vial without a traceable certificate is an anonymous vial regardless of where it came from.
Residual moisture is the dominant determinant of solid-state stability, which is why desiccants accompany lyophilised material.
Keep the desiccant with the vial and the certificate with the lot code.
edited 16 Jul 2024 by RP_C18 — tightened the wording; no substantive change