You can write what you like in your log book just be very very very careful about trying to claim time illegally towards the issue or revalidation of a rating.......
By illegal I mean one of, but not limited to, 2 pilots claiming the same flight time, a pilot claiming P2 in an aircraft certified for only one crew, claiming flight time in an aircraft as commander that you are not qualified to fly or as a student without an instructor. Thats a few but the list can go on.
Before we generate even more pages of drivel. The answer is simple, there is no P2 in a SEP regardless of what duties you performed.