it's hard to tell you how to 'wire' it exactly, as it depends on what 'type' of inverter the factory installed, and what it controls.
Some are 'pass thru' Inverters which 'pass thru' 120v Shore Power or Generator Power when they are available. In this case, the Inverter not only gets it's main power from the House batteries, but will also have a 120v hot wire coming in from the Main Panel.
Others do not 'pass thru' 120v power, but are just there for a single appliance, like the residential 120v fridge. These would only require a 12v battery cable hookup from the House battery bank. They usually have an outlet built into them, also, although they may have 120v wiring out for a powered wiring circuit, for several outlets.
two Campers, two Electric cars
former diesel pusher traveler