The answer to the OP's question comes from considering who will own the accident or incident if the trip does not go well - this is the person who signed for the aircraft and that person therefore logs P1. In the club world this is usually the FI. It's not possible for two people to log P1 so the person being checked must be Pu/t (P1/s is not an option unless the flight is a test with an FE).
I've met several club pilots who are unhappy with this situation and use P1/s or P1, but this is outwith the rules.
HFD