The inverter can be modeled like this:
View attachment 139060
Notice that the Blue and the Brown wires are isolated from the case and the neutral is not used at all. Also note that the charging circuitry can take anything from 90-265V AC.
Personally, I would not try to make an adaptor if I wanted to run this on 120V. Instead, I would replace the plug.
View attachment 139061
It does not matter electrically, but notice that putting the blue wire to the neutral prong of the plug best follows the international standard.
This could use a standard 15A plug but the charger would have to be configured to limit the input to 15 Amp. However, I would seriously consider using a higher amperage plug. A 20 amp would still require limiting the charger but a 30A plug would allow the charger to operate at it's full 120V capability.