A typical 1500WATT INVERTER will need to be fed from your battery bank using 4AWG CABLE with at least an inline 150AMP DC FUSE. 2AWG CABLE would probably be better... I would keep the length of the 12VDC HOT and GND CABLEs to less than five feet long. This information should be in the installation manual.
When the 1500WATT INVERTER is fully loaded down it will draw around at least 121 AMPS DC CURRENT plus inefficiencies.
The Air Conditioner will have a pretty good surge before starting up.
The two AGM 12VDC batteries in parallel will have 250AHs capacity but you need to check the battery specs on how long the battery bank will produce 12VDC at the 121 AMPS draw to know how long the air conditioner will run before discharging the batteries below their 50% capacity...
INVERTERS are known to be battery hogs big time...
Roy Ken