If we ever figure out FTL travel, FTL communication is relatively simple: worst case, you send your message to a ship (possibly a drone) with instructions to FTL-travel to the destination and deliver the message. It’s kind of the high-tech equivalent of a man on a horse delivering a sealed parchment, but it’d work.

If by that point we haven’t figured out a better way to do it, at the very least we should have that method available.