Puerto Rico residents must invest in Puerto Rican Roth IRAs. This is because Roth IRAs in PR have their own special rules in terms of amount of money withheld and more importantly, the type of securities they are able to invest that includes a percentage of Puerto Rico securities that need to be in the fund to be considered a retirement vehicle.
This is an issue for those that opened Roth IRAs or 401ks in the USA and move the Puerto Rico being that withdrawals from US Roths are taxable in Puerto Rico, one end up paying taxes on three jurisdictions rather than two. Therefore, those that live in the US mainland and are planning to become a bona fide resident of Puerto Rico are better off investing in a traditional IRA or 401k during their working years.
One can opt to convert from an US traditional IRA to a Puerto Rico Roth, but one has to be aware of the conditions and expenses of doing so. What I've personally seen is advised against doing it.
If you live in PR, that is handled by your employer (401k plans) or through local banks. They take care of the legalities and compliance with PR tax laws. Puerto Ricans can invest in Roth CD or Securities IRAS in any of the major banks (Oriental, First Bank or Popular, for example). Check their offerings decide what it is best on your situation.
Are Puerto Rican residents able to invest their Roth IRA assets in any investment company in the continental United States?
In summary, as long as the company has nexus in Puerto Rico, you should be able to do so. The only two that I can think of is UBS and Charles Schwab; they both have offices in Hato Rey. UBS for sure, I remember reading their prospectus but I am not sure about Charles Schwab. I know folks that they invest in Vanguard because they opened accounts in the USA and moved to PR, but most likely they're traditional and not Roths. For that, the rules to determine income source apply. Check IRS Publication 570 for details.