This is silly, yes. The answer is making PR a state, but historically they haven't wanted to be one and Washington has been hesitant to make them one. Here is a short video on the matter which coincidentally was published a few days ago: https://www.youtube.com/watch?v=Mk6JrUYLyWw
If a US citizen from Idaho moves to France, they likewise don't become a citizen of France
Is the problem that US citizens that move from Idaho to PR are not allowed to vote at their previous address, but US citizens who move from Idaho to France are?
Heck, I've voted absentee in my home county in California once while I was living in a different county in California.
It is worth noting that the last three referendums on the topic in PR all ended with a result indicating support for becoming a state, the final one in 2020 being unambiguously clear on the matter.