The relevant detail is that read the cake before you touch the vial. An intact, opaque, evenly distributed puck that sits proud of the vial base is what a good lyophilisation cycle produces. Anything else — collapse, melt-back at the stopper, a glassy film, a cake that has slumped to one side — is evidence about the cycle, the shipping, or both.
The practical summary: fine gauge, gentle swirl, diluent down the wall, room temperature before drawing.
On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle.
Do the arithmetic twice, ideally with someone else doing it independently.