Can a US permanent resident travel to Puerto Rico ...

I can't find a specific answer to your question on the U.S. Customs & Border Protection website.  However, the website has these statements, which may be helpful to you:

• "Lawful Permanent Residents (Green card holder's) do NOT need a passport to enter the United States" (from elsewhere in the Western Hemisphere) (http://help.cbp.gov/cgi-bin/customs.cfg/php/enduser/std_adp.php?p_faqid=74)

• "If you are a green card holder and you do not stay outside the U.S. for 1 year or more you should have either your green card (INS Form I-551, or your returning resident visa to re-enter the United States. You are not required to present your unexpired passport, however, it is not a bad idea to carry it with you." (http://help.cbp.gov/cgi-bin/customs.cfg/php/enduser/std_adp.php?p_faqid=820)

• "U.S. territories include the following: Guam, Puerto Rico, the U.S. Virgin Islands, American Samoa, Swains Island and the Commonwealth of the Northern Mariana Islands." "These territories are a part of the United States."  (http://help.cbp.gov/cgi-bin/customs.cfg/php/enduser/std_adp.php?p_faqid=980)

You might want to contact the CBP to ask whether there's any other information on this question.