Players should stop “capturing the king”. It’s a bad habit. Just claim the illegal move. It may not matter much in bughouse, but it’s a bad habit that could have repercussions in more serious play. Since this is bughouse, I would accept this as an alternative method of “claiming illegal move” and not worry about the actual legality of the king capture. I would base this only on the validity of whether Player B had made an illegal move or not. Now if Player B’s move actually was legal, perhaps now we start to determine the validity of Player A’s move. Like I said “capturing the king” is a bad habit.
Once these players graduate to FIDE blitz, then Player A loses.