It is more likely that a stray dog will adopt you than the other way around.Â
There has long been a terrible stray dog problem in PR, though at least by my observation it is not as bad as it was five years ago. There are a number of rescue organizations that have been collecting strays and shipping them north for adoption. Save a Sato, the Sato Project, All Sato Rescue are a few. There are also numerous shelters brimming with animals. And there are many just roaming the streets.
Ours found us. Chewed up by a pack it showed up in bad shape. After a significant contribution to the local veterinary economy, the dog is great and won't leave my wife's side.
Taking any pet on an airplane is a challenge. JetBlue will let you take a small pet <20lbs in the cabin for $120 and that works great. Other airlines are not so pet-friendly. Ours is 30lbs and has to go in a crate in baggage and that is a royal pain with lots of complications relating to heat restrictions, drop off locations, etc. From a paperwork point of view, you will need a recent health letter from a vet that is easy to get. The fares for the animal are usually more than yours.