Ebbie;
The flight is a check ride, the CFI is P1. Your ex-BA Captain would understand this from LPC/OPC and line check days. He may be fully qualified to fly the aircraft, and vastly more experienced than the trainer, but the CFI is P1 and should be the guy who signs the tech log.
I do an LPC/OPC, IRR and line check on each type I fly for a living, the training captain is the P1, when I get a check ride with the local flying club their instructor is always P1
SND