Puerto Rico is part of the
USA. Puerto Rican's are US citizens, just like you are(I assume). All aspects are the same as the US. You could buy and document a boat in the Chesapeake, sail it to Puerto Rico, and do nothing else because you are still in the
USA.
If you are NOT a US citizen but a foreign national that resides here, then you can't own a US flagged boat. You need to flag and document the boat for whatever country you are a citizen of and then comply with the limits of keeping a foreign boat in the US.
If you intend to keep the boat year long in PR, then
insurance will be difficult to impossible and expensive. And rightly so, as it is no longer "insurance" against the unexpected, because destruction of your boat in a
hurricane is a "when" question, not an "if" question as far as insurance policies go.