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Best to get a small digital multimeter and do some testing first. Start with all the service breakers and the AC outlets of your inverter to find out if the source is the issue. Then we can move to looking elsewhere. A meter is about $20 or so at most hardware stores and easy to use. Be sure that the GFCI isn't installed backwards or it won't work. Let me know when you are ready to test and I can direct you here. All follow ups are included in our fee. And I don't know of any wiring diagrams available for that unit.
Just checking back in to see if you were able to get this resolved or so you still need some additional input from me here?