I looked into this a couple of years ago and was set up to hire from a company in Kingston. They told me that to get a Jamaican licence I simply had to pass the air law exam, but when I spoke directly to the Jamaican CAA I was told I also needed a Jamaican medical. This made it not worth while. I don't see why you cannot hire dual, but I guess you cannot then be P1. I was going the meet the aircraft at Boscobel, a small airfield near Ocho Rios.