The best/fastest way is to use your onboard 12v
converter/charger to charge the batteries by plugging the shore power cable into the generator letting it run. Depending on how low the batteries are and whether you have an upgraded converter or the original Parallax, it may take a couple of hours of runtime to fully charge the batteries.
Several people report being able to use the AC with that generator if they're very careful about load. I suspect that a heavy charging load plus the AC would be a bit much, but it'll certainly run the converter plus vent fans and lights, water pump, etc.