He may legally marry her as long as he follows Filipino marriage laws -- he needs no special permission to get married.

To bring her back to the U.S. after marriage, she will have to remain in the Philippines and seek Consular Process for her Green Card petition, a process that may take up to 1 year. If the goal is for her to immigrate to the U.S., an alternative to consider is seeking a fiancée visa, then having her travel to the U.S. for marriage and seeking to adjust her status within the U.S. -- a fiancé visa can generally be obtained in a matter of months.