Absentee voting in PR?

So, as I understand it, Puerto Ricans are American citizens, and get to do most of the things us in the 50 states get to do except vote for President. However, as American citizens, they could move to, say, Ohio, get residency and then vote, right?
It stands to reason then that people from one of the states who moves to Puerto Rico would then lose their right to vote?

I’m in Oregon, and if I move to France, I can still register absentee and vote for President, so maybe if I move to PR I could register absentee and still vote, couldn’t I? So taking this one step further, could a Puerto Rican move to the mainland, stay a while (maybe go to college or something) get the right to vote, and then move back to Puerto Rico and vote absentee? Therefore, they’d be a Puerto Rican in Puerto Rico who had all the rights of the average American citizen including the right to vote for President–or am I wrong?

Yup.

Ah, but Puerto Rico is not a foreign country. It is a territory of the US that lacks an electoral college. Although I am curious… Do expats in other countries (barring things like college, military service, or diplomatic work) get to keep their right to vote absentee in the US? Or is it one of those things lost when they permanently move elsewhere? The reason is that a Puerto Rican that moves to the mainland for some purposes (college one of them) can still vote absentee. That is what I do.

But where will the permanent residency be? If the person’s permanent residency is in some county in GA, and they move temporarily to Puerto Rico, I can see them getting an absentee ballot. But if your permanent residency is in a completely different territory…