couldn't see the face book pictures, don't belong to FB
many people use photobucket or one of the other picture hosting sites
anyway good thing you found out the 'Hot" power cord, yes that would fry your inverter
your new Electrician will remove the 'hot cord spliced in' and can a install the transfer switch
the switch can go near the fridge
the wire can run from the switch to the inverter and stay permanently plugged in
will function 'electrically' safe
the TS will switch between the two 120v sources
Yes you can get inverter with built in TS, but then 120v power has to be run to the inverter then back to fridge
let your electrician decide which will be less costly and best to do for you