Technically just about 2-3 weeks, but I would suggest to put in a transfer in a month or more ahead of time just to make sure everything is done right. Stay on top of the HR as well to make sure they are on top of it.
If you are awaiting to see if you get a new position, generally promotions do not transfer unless there is an open position and the new store approves you at the position as well. Some stores may want to interview you.