Start with the physical state, because it changes the answer completely and is the first thing to establish.
A pack that arrived hard tells you about the last day of transit only, since it will have melted and, if the ambient dropped, partially refrozen.
Once the parcel arrives, the domestic leg is the controllable part: get it into the refrigerator promptly rather than leaving it in a warm hallway for a day.
Solid-state stability of lyophilised peptides at ambient temperature is documented in formulation studies with residual moisture as the dominant variable.
Reconstituted material has a genuine cold-chain requirement and it starts the moment water is added.
A liquefied pack is expected. It is not evidence of a problem.