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

If the converter actually puts 45 amps into the battery you might overload the inverter. A single test will confirm with no harm. Of course the inverter would need to be hardwired to the vehicle start battery. And inverters don't really like heat under the hood. If you plan to do this while idling stationary the alternator may not keep up. Otherwise you are good to go. No harm to the alternator.