Agree, his written description is what I was referring to.
The graphic represents just one way an inverter could be wired (and one I would never use).
Again, we need the OP to let us know if his inverter has an internal transfer switch/pass through feature so we can intelligently address the issue. There will also be other things that he will NOT want to be able to power from the inverter in addition to charger/converter such as A/C, water heater electric element, etc, as they would either overload the inverter and/or deplete batteries very quickly.
Again, more information on exactly what equipment you have and what you want to be able to do would get you better answers.