GTI captures beam tech from Shivans, incorporates beams into Hades but continue to develop them. GTA destroys Hades and halts the rebellion, sifts through what tech and projects they could find, destroys what they don't like, keeps what they do... including beams. GTA's recovery of GTI's beam development is incomplete, but enough to give them a starting point. Some years later, beam tech is matured enough to mount on GTVA ships. The only thing that raises an eyebrow story-wise, is that the Shivans decide to equip beams to their cap-ships across the board at the same time the GTVA does... AAA too. That's somewhat coincidental timing. Of course, the real reason was Volition wanting to spice things up visually, and perhaps find a way to make cap-ship engagements more interesting and less drawn-out.