Verify if your inverter has a neutral-ground bond. If so, your schematic should work. To verify: with the inverter disconnected from the battery, use a multimeter set to measure resistance at it's lowest setting (or if it has continuity test setting use that). Check between the neutral and the ground connections. Should read zero or pretty close to zero. If it doesn't read anything, then you don't have a N-G bond and will need to provide it on the inverter side of the switch. If you don't have the N-G bond, you will have an open ground situation which is a safety issue. Do not bond the neutral to the ground anywhere else except at the inverter.
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Thanks James. I have one more question: If I were to use a SPDT relay instead, could I tie the neutral from shore mains to neutral on the inverter? I come from the 12VDC world thinking this would be like tying ground common. Of course only if the ground and neutral don't connect on the inverter.