The short version: a spent cold pack on arrival is expected, the solid does not mind, and the pack was never going to last twelve days.
A single-use temperature logger costs a few pounds, records the whole journey and converts an argument into a record. If the history matters, this is the answer.
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.
Phase-change pack hold time is a function of mass, latent heat and insulation, and published figures for small parcels are on the order of one to two days.
Buy a logger if you actually want to know. Everything else is inference.