What would happen to Puerto Rico's political parties if it became the 51st state? Is there any historical precedent for what happens?
They would almost certainly fold into the national parties. It would be very difficult to remain independent once national politics come into play.
Puerto Rico would gain a House seat and two Senators. Candidates would take major party funding to campaign (thus assuring they caucus with that party). Those politicians would likely then draw their political party counterparts to the national parties (which already closely mirror mainland US parties), where political funding and organization would be far more than local politics would raise. On the local level some PR parties would remain, but it would be harder for them not to nationalize against opponents who have already done so.