One, some of you seem to believe that Ubuntu citizens will magically abandon their culture and beliefs if the GTVA wins, I doubt that and if the GTVA pushes too hard it might end up on a second civil war with Sol. (This has happened countless times in history)
Second, Space is a big place, the UEF could literally send probes at the edge of the solar system and have them transmit records and decoded GTVA transmission about the war, yes it would take centuries for them to reach GTVA space, they could also storm the node with as many fighters as possible and go straight to Delta Serp. and start transmitting, they could also go to other systems and do the same (This is all considering the ships having system drives.)
Third, who says the GTVA will win the war?