Lithium Iron Phosphate 12v battery swap?

I am without power at my house due to the Park Fire in California well likely be without power and electricity for weeks or months. Of course I will eventually get a generator up here to my property but I'm wondering with the materials I have on hand if I can run my refrigerator.I have a 2010 Prius and separately I have a 100 amp hour lithium iron phosphate battery with two solar panels. But the panels cannot maintain the charge on the battery when running large things like a refrigerator. Since the Prius can charge a 12 volt battery and just run the engine when that goes low would it be possible for me to connect my lithium iron phosphate battery to the Prius as a replacement to the stock 12 volt battery? I could then power my 2000 watt inverter directly from that battery. this would just be a temporary setup but the idea would be to be able to run my refrigerator. I know when when the Li battery is fully charged My 2000 w inverter has no problem running my refrigerator... So will this work? Or will putting in a lithium 12 volt battery somehow damage the charge system?