Pilot A signs for the aircraft; so he needs to be taking it back in one piece
Under UK law there is no requirement to sign for an aircraft, there is however a requirement to sign after the flight. But, we are now operating aircraft under EU Law where there seem to be different practices in every State and nobody knows where to find the rules. In many States, the Aircraft Log is not completed until after the flight, so who apart from the two pilots know who is PIC?
If one pilot is not current then he is a passenger and the answer is simple, the only legal pilot is PIC but, is there any paperwork to prove this and did he know he was PIC throughout?
This thread highlights potential issues if two pilots do fly together and share the responsibility. If something goes wrong, they may equally share the blame, and any liability that it might incur, unless they have had the foresight to document who is doing what and when before they take off.