Don't have the manual, but the product description on Amazon says:
Amazon.com: AMPINVT 3000W Peak 9000W Pure Sine Wave Power Inverter DC 12V to AC 110V Ouput Converter with Battery AC Charger 60A max Adjustable,Off Grid Low Frequency Solar Inverter for Camping RV: Garden & Outdoor
www.amazon.com
5 working modes:
1. AC Input Priority--- Preferential use of municipal electricity, (household 110V AC) municipal power outage to battery power supply, municipal power to return to municipal power supply!
2. Battery priority mode----Priority should be given to battery power supply. After low voltage protection, the battery will be transferred to market power supply. When the battery is full, the battery will be transferred back to battery power.
3. ECO Mode---Load < 10% automatic sleep and stop output, load > 10% automatic boot back to normal inversion.
4. Generator Mode---Use an unstable AC voltage (such as an alternator) through the inverter's AVR regulator to make the output voltage more stable!
5. Unattended Mode---When the battery is low voltage, the inverter goes into standby state(Power saving state). When the battery restores the voltage value set by yourself (such as solar charging), the inverter will restore the normal output of the inverter, and realize unattended full automatic operation!
I presume the manual describes how to set the operating mode. The closest to your desired intent appears to be mode 2.