The Fridge battery wire probably goes up front
To a post on one of the solenoids,
It is also possible that it goes directly to the wiring from the converter that leads to the house batteries up front, is your circuit breaker power center in the kitchen area near the fridge, your converter for charging is part of the power center
It is being charged by the converter when the generator is on , or plugged into shore power just like the two house batteries up front,
Most likely the 3rd battery was not installed at the same time as the fridge and inverter, but the voltage drop from the long wiring path (all the way up front) was too much and the inverter would give a low voltage fail when the fridge kicked on, so the third house battery was installed at the fridge to alleviate the problem
All 3 house batteries are parallel, and supply power to fridge and house unless some how disconnected from each other,
The inverter is dedicated to the fridge, but that battery is Not the only one powering the inverter
The blue finned box with battery cables is the diode based battery isolator that charges your batteries from the ALTERNATOR when the engine is running, it keeps the house batteries separated from the chassis/engine battery
