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You do not need a visa or passport to travel to Puerto Rico from the USA, whatever your nationality. It is considered a domestic flight. As long as you don’t plan to travel to the British Virgin Islands or some other island, you won’t need a passport.
Once in a very rare while you may encounter Customs and Border Protection officers who will ask you if you are a citizen. If you are not, be prepared to show your passport, greencard or some other document to prove you are legally living in the US. But such a check is exceedingly rare.