Look up your countries regs and save some bandwith.
In every country where I have flown, on their register, then the only PIC, who can log PIC, is the nominated captain who has the authority to sign for the aeroplane, both tech log and load sheet and that authority is only given to a fully qualified captain, on a multi crew aeroplane that qualification involves passing a command course. I would be very surprised if the FAA was any different as there is the legal aspect to be considered too and a type rated qualified FO, appointed as such, cannot be held responsible as PIC.