Why does a computer restart when the power shifts from an inverter to AC mains. Note - computer is connected to UPS which is connected to AC mains-inverter?

It sounds like the UPS is not working. Check and make sure that the computer is plugged into the UPS and has not been mistakenly plugged into AC power. Have the batteries been looked after since the UPS system has been installed. There should be a battery low light on the unit to tell the status of the batteries. There should also be a low voltage level alarm on the UPS, make sure that the safety warnings have not been shut off. There is definitely a break in voltage on switch over from AC to emergency power hence the computer restart.