Is there immigration in Puerto Rico for flights from the USA?

I am not a US citizen so would I need to show my green card?

I use a CA DL for domestic travel and use my Green Card (via GE) for getting back into the USA. US immigration does not care abut my passport.

Rest of world I use my passport (and immigration folks spend an age looking at it due to all the foreign stamps and visas).

Would not have occurred to me to take my passport with me to a US territory.