No they will not be able to transfer the approval because it is going to be tied to a specific vehicle. They will need to rerun a credit application with the vehicle information at the next dealership. But the approval should at least signal that financing would be available. I would bear in mind whatever interest rate you were offered on the first loan and don't let another dealer tell you that you need to pay significantly more unless the first one was a specific promotion through the manufacturer. Ally is the old GMAC financing so just because GM may have 0.9% special doesn't mean that Ford or Hyundai will match it for example.
Starting Score: 500's