But shouldn't it be wired in such a way that when it is working as an inverter it will not feed the 240v side of the Truma heater? That will knacker the batteries in no time whether lead or Lithium..It is an inverter charger.
When your on hook up it is an 80 amp Multi stage battery charger
When there is no hook up it is an inverter
When there is hook up and you require more power than the hook up can give you, it "makes up the difference"