how is that possible...? the inverter must always put out the maximun it recive from pv, every off grid system or also a mppt must always give the maximum and how can know the inverter know that the charger needs more...?
Inverter just delivers 120VAC. Charger draws current from it. Unless inverter (or generator or grid circuit breaker) can't supply that much.
If you have an AC powered battery charger trying to put say 100A into a 50v battery, it needs 5kW.
If you have 3kW coming from PV to a battery less inverter, it will support AC loads up to 3kW. Loaded with 5kW, output collapses.
This can work if you way over-panel, e.g. have 5kW STC of panels and 1kW (20A, 50V) battery charger.
It can work if you have a PV + battery system, feeding battery charger. With a 5kW battery inverter, it will keep feeding that 100A 50V battery charger until its own battery is drained.
But what you really want is MPPT connected to PV, with output delivering variable current to battery, whatever is available. That is an SCC.
OK, Make Blue Sky can do it for $155, or Midnight Classic can do it for $800. Your choice.