The inverter connection is kind of tricky. It has an automatic transfer switch. If shore power/generator is available, it cuts itself off the circuit and cuts shore/generator power through. If there is no shore/generator power, it connects to the circuit (refrigerator, some outlets and some appliances).
You won't see a breaker for its 120Vac power on the panel diagram that WMTire posted. Its breaker is on the inverter itself. If that breaker is tripped, the refrigerator and possibly some outlets and appliances won't run, even though the inverter itself is not producing power.
One question: You said the Samsung refrigerator has power. That suggests that the transfer switch IS working, and the theory above is incomplete. But it wouldn't hurt to check voltage at the inverter and transfer switch.
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