"Sole manipulator of the controls" seems to be the key here. They could have said "Pilot in Command" (as they do in SEP revalidation for example) but chose not to.
So I believe you can jump in with him, log three circuits as PIC, while your friend does the take-offs and landings, then you switch command and he logs the time from then on, having gained his experience.
Subject to Group/Insurance/POH restrictions as others have mentioned, but IMHO not LASORS.