Financed Vehicle

Just tell them you would like to transport your vehicle to PR. They will either allow it and give you an authorization form or reject it. If they reject it, you can payoff the balance or sell the car or not move.

If military it is easier to get the permission, also if military let the arrange for the transportation of the vehicle, it is part of the package and you will not be taxed when the car arrives in PR.

If not military, when the vehicle arrives in PR you will need to pay the taxes, likely in the thousands