Re: inverter problem
As 90% from the questions from this site, it contain an incomplete description of the inverter and that let the answerer to imagine his own version of the problem.
Completely useless.
Even you didn't look carefully enough and there is more than one transformer, or the batery is not charged from this inverter.
Usually old proffesional inverters with sinusoidal output (not rectangular, not DC output) have two inverting stages, like 220VAC to 12V, 48V or 60V DC and back to 230V AC. This structure is charging indeed the acumulator.
But an inverter 12V DC to 230VAC has absolutely no option to charge the acumulator connected on the input unless a completely charging circuit from main 220V AC is used inside the charger, so then it becomes a 230VAc to 230VAC inverter.