Fair enough. Sounds like A is going to have to decide whether they talk to B directly, complain to the supervisor that B still isn’t meeting expectations, or drop it. But keeping you in the middle isn’t going to solve the problem and it needs to stop. You can say that firmly but nicely and with validation. (The validation is important to maintaining your relationship with A.)
At the end of the day, this sounds like a failure at the management level. If B is known to be underperforming, it’s on management to either find a way to help B improve or replace B. Management’s failure here is hurting all 3 of you. A has a right to be pissed. B needs guidance or the boot. And you need to be free of this mess.