OK so the manual for the MSH3012M does say charger input is 60 to 140 vac and 50 to 70 Hz on page 43 appendix A-1.
MSH3012M manualThe confusion I have is the output of the inverter is 60 Hz. I wonder if it will not sync up or pass through 50 Hz as this is part of the inverter specs not the charging specs.
I did not see a charge only specification that allows 50-70 Hz to the charger but stops prevents pass through. Appears the charger comes after the pass through relay and I think the electronics are looking for 60 Hz before that relay will close.
Have you tried with the inverter section off? That would be my best guess that the inverter and the 50 Hz do not get along. You somehow want charging only.