Good answer. Verify that only those items you want to be able to run off the inverter are wired through it.
Certainly A/C's should not be wired through it.
If run through the inverter, you risk doing a lot of $$$ worth of damage to your electrical equipment.
Tell us exactly what inverter you have, and whether it is an inverter/charger AND whether it has a "pass through" feature and if you still have a separate converter, what do you have.
Then we can give advice on the way it should be wired.