[psandman]

In my room if there is a player ready to take the vacant seat and you want the seat you must move immediately - the exception being that if your seat is in such a spot that the new player would be unable to take a hand in the seat you can play out the hands.

In the case you give if Player A gets up and moves now the new player could sit in player A's seat and take the Big Blind. As such Player A should move immediately, but often times here the player will not object to Player A staying since the new Player prefers to come in after the button anyway.