PICUS is logged by a co-pilot performing the duties of PIC in multi pilot operations.
The BN2 is single pilot so you can't log PICUS
Your scenario is very straightforward as there is no FI/CRI onboard: only one of you can be PIC and log the time. Even though you are receiving training, it's line training not flight training: you're flying as PIC in an airplane for which you have a licence, so the flight time goes in your logbook not his/hers.