Here is a list of shippers that will move your car. We have not vetted these companies to know if they should be recommended or not. In addition, there is an import tax charged for bringing a car into Puerto Rico, even if its a used car that you already own. No items are allowed inside the vehicles except for one car jack and one spare tire.
The port will not accept vehicles with more than ¼, one quarter full, tank of gas.
San Juan to/from Jacksonville FL $1706
Ft Lauderdale/Port Everglades FL $1804
Jacksonville to San Juan $1105+$75 = $1180