It seems to me the UEF just might manage to field a warship (maybe even a few) with beam cannons--and those might even be the equivalent of anything the GTVA has in the field. They probably have salvaged parts, either from the Lucifer, GTVA ships destroyed in Sol, or defectors. They have GTVA personnel with working knowledge of GTVA technology who defected at the beginning of the war. (More on this later.) But it's highly likely that beyond a ship or two that might have the tech, beam cannons are just not going to be in the UEF's wheelhouse anytime soon.
BP lore and word of god suggest that reverse-engineering beam weapons would be cost-prohibitive for the UEF, especially as regards the newer "blue beams" Terran ships use; it's not just a matter of swapping out a few parts in the weapons turrets. They lack the tech base for beam cannon production on any scale, though as I said, they might salvage a few as "prototypes." It's a whole different tech tree they may have never considered.
A Word Regarding GTVA Defectors:
After Age of Aquarius, three ships and an unspecified number of personnel defected to the UEF. This included a cruiser, a corvette, one logistics ship, and at least some high-level command personnel. There were several examples of blue-beam technology available to study*, and at least point UEF researchers in the right directions. Repair technicians might be forthcoming about information concerning these weapons and their predecessors. Higher level personnel such as Bei Sr and Jr might have known enough to point the research teams to even more specific things. (I'm assuming that GTVA officers have at least some cross-training in the science and engineering of their ships, not unlike modern naval personnel.)
Admiral Bei has been in Sol for 18 months and change. He's on speaking terms with at least one Council member. I find it likely that if Bei, the Council Elders, the UEF Admiralty, the Fedayeen, and whatever others would be privy to the information he has--if most of those people thought beam weapons would save the UEF from the GTVA's invasion, they would have fast-tracked its development as quickly as they could.
*Did GTVA planners specifically not include older designs to keep older beam weapons away from the UEF--on the off chance those beam weapons could be easily swapped in?