How did you determine the Fuse was OK. At the terminals of my Invertor/ Convertor is a fuse. It is a bolted connection using 5/16 or 3/8 studs hidden by a plastic cover.
But reading again that your convertor is working and batteries are 13 volts leads me to ask are the Convertor and Inverter separate units. You may have two fuses. The fuses should be found in the Positive (Red) cables.