John de Wit
Player A now has one last round to try and get enough Brains to beat 13.
This is incorrect. From the rulesheet (emphasis added):
"Play until someone reaches 13 Brains. Then finish the round. Whoever
has the most Brains at the end of that round is the winner."
If player 2 rolls 13, he ends the round. Player one does not get a chance to catch up. Players later in the turn order than the first to hit 13 are given their last turn so all players have an equal number of turns.