Of course. I'm not aware of any current laws of the USA that forbids mail from being sent anywhere worldwide. Of course, we have no control over unfriendly nations from censoring or confiscating what we mail. Puerto Rico is not in such category.
The only thing that can't be ship by post office is anything hazardous or dangerous please refer to the usps website on what you can ship and what cant you ship
Does this post office do passport renewal?
Yes, you can. It's a commonwealth of the U.S., since you can send mail international, it's no different.
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