To re-iterate, you have a 240/120 V 4-wire circuit and a 120 V circuit.
The only POSSIBLE thing you could do is to convert the 120V inverter output into a 240 center-tapped output by means of a transformer.
Two high rated 7.5 KVA instead of 2, but this is similar to what you would need with correct outdoor enclosure, etc. SQUARE D 7S6FIS Transformer 7.5kva
Grainger is Wholesale only.