I called the Police Headquarters (787) 793-1234, Firearms Licensing Division, and the person who answered the phone told me that they expect to have more definite answers to reciprocity and other questions after January 2nd.
The applicable section in the new law is translated as follows:
Puerto Rico Weapons Act of 2020
Law No. 168 of December 11, 2019
CHAPTER II LICENSE AND REGULATION
Article 2.02.-Weapons License.
Article 2.02. (E) (9) Persons with a weapons license from other jurisdictions, in order to have the same rights and privileges enjoyed by persons with a weapons license from Puerto Rico, shall comply with the requirements of this Act. At the same time, they must inform the Weapons Licensing Office, in case they intend to introduce one or more weapons and / or ammunition to Puerto Rico. The Commissioner shall provide through regulations, the manner in which said notification will be made.
Apparently the Police Commissioner is still working on the procedures… I plan to travel there for Spring Break and hopefully we will know by then.