If the GTVA wins from the UEF, I imagine the GTVA would use 85% of the UEF facilities to produce more GTVA ships and fighters, while using a mere 15% of facilities and labs to research the possible application of UEF designs and weaponry for use in warfare against the Shivans. My money would be on beam weapons though, not mass drivers. Beam weapons have only now begun to look somewhat refined, they can probably be developed much further to be REALLY efficient.
Also, UEF material would be difficult to maintain. You would probably need to modify all your GTVA facilities to be remotely able of maintaining UEF vessels. And since refitting UEF ships to GTVA standards would be costly and carry a constant risk of having incompatibility issues, not to mention a chance to perform sub-par, wouldn't they just likely scrap 70% of the UEF fleet in favour of keeping the larger vessels as a defense fleet for Sol? Sol has facilities which are already compatible with UEF vessels.
Or, I can imagine that decommissioning the UEF's capital ships will go a long way in propaganda, spreading stories that GTVA capital ships are far more advanced. That way the Sol citizens would somewhat feel the GTVA presence gives them better chances against Shivans, once GTVA propaganda kicks in.