[SOLVED] Can an inverter on a car charge the house battery?

A 45 amp converter is fully capable of putting 45 amps into the G24 battery. Although depending
on the converter brand and charging profile and the 12v wiring you may not get 45 amps for long or only half that amount. A good converter could put a solid 45 amps in for maybe 30 minutes before the battery acceptance rate causes the amps to begin tapering off.

If you were buying a separate charger a 10 amp rated unit would work perfectly good.