If it is a successful check, then I tell the pilot to book it as P1 and I will countersign it if required. I then don't book any time myself.
If it is unsuccessful, i.e I had to intervene with decision making or handling at any time in the interests of flight safety, then it is Put and I would book P1 as an instructor.
P1s, as stated before, is only for successful flight tests with an examiner.