You can't have it both ways, unless you want to have this discussion all over again each time a club check is being performed. So if the POB specifies that a designated PPL can perform club checks, then in all cases the hirer should be P1, even if the guy in the RHS happens to be an FI. And if the POB specifies that clubchecks can only be performed by FIs (as my club does), you can (but do not have to) specify that the FI is P1, and the hirer Pu/t.
I think that you will find that in the cases where the check is done by a pilot who does not hold a valid instructor rating then the pilot who is being checked can not log any time but can only record the take-off and landings they completed as sole manipulator of the controls.
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I am surprised to see that there is no general objection to having to complete a 28 day check the only objection being to having to log dual time for the 10 to 40 minutes is takes to complete such a check.
Regards,
DFC