BBC (on the net) has a sound clip about the case (News, America, search 'Cuban music'), made over a year ago and revived since the case has been re-opened. A British judge has moved to Cuba and is hearing witnesses.

The fight with Peermusic (an international company based in U. S. and very strong in Latin American as well as North American music) is over UK rights which are held through a Cuban-based music company, and which are claimed by Peermusic Inc.
Before the Cuban revolution, Ralph Peer and his developing company had signed up some 600 Cuban musicians. Do these rights prevail, or subsequent handing over to a Cuban group after the revolution? Peer's contracts long predate the Social Club.

I don't believe the case will affect copyrights in the U. S., held by Peermusic. Peermusic is a large and active company; recently they have acquired through purchase the rights of Caribbean Waves and Crossing Waves, which include Celia Cruz and Tito Puente among others.

The A. P. Carter and Carter Family rights held by Peermusic are extremely lucrative and have paid well to the Family and their assigns.