You have made confusing statements and it's hard to know what's going where with the wiring
Your inverter has a GFI out let on the front
WHAT'S ON THE BACK?
Is there a 120v cord with male plug ?
If yes then it has 120v power coming in and has pass thru
Just plug the cord from the front, into the power outlet feeding the inverter
If there is only red and black 12v wires going to the battery, then no pass thru
You can take the CORD END that used to plug into the front of the inverter and plug that into an extension cord
Take pictures of ALL the inverter wiring connections and post them here
Do Not use a cord with two male ends to back feed into your RV circuits