Don't confuse converter/charger
With inverter
You could have a converter only, or you could have a combo inverter converter
But you haven't given us any equipment numbers
Make and model number of fridge
Make and model number of converter? Inverter?
Does the tv work, with out shore power ,? If yes then you have an inverter some where that may not be attached to the fridge
If no, then you do not have an inverter
RV fridge with lp elect our auto
Must be on lp or auto
To make sure it gets cold and it is slow, takes time
RV fridge is very seldom connected to the inverter, although in some model the ice maker it's connected to an inverter
The avg RV lp fridge draws too much power on electric to run from an inverter and only one or two batteries and no generator,,