Foggy is right - there are a lot of myths about logging time, particularly P1S, which isn't clear even after reading the relevant documents.
But there is no doubt at all that, under JAR, only one person is P1 in these cases. If your instructor logged P1, you can't. If he didn't, you can. This should have been agreed between you before the flight.
Personally, I always assume an instructor is going to log P1 and I log P1T unless the instructor tells me otherwise, and I often confirm this by asking "you're the captain, right?" It means that if there are any decisions to be made, e.g. in an emergency, the instructor's decision overrides mine. Which makes sense.
FFF
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