[Arkware]

I think we have a common term issue.
An Inverter uses 12 volts DC, batteries, to make 110 volt AC. (shore power)
A converter takes 110 volts AC, shore power, and 'converts' it to 12 volts DC to charge the batteries.
The Converter that came in your rig will happily charge/maintain an AGM battery.
Since you are plugged in, I suggest you let the converter keep the battery charged.

My 2015 converter/Power control center is Progressive Dynamics, Mdl: PD4500 series.
Yours should be the same or close to the same.

Hope this helps,