“Cigarette” plugs are rarely rated for more than 10 Amps which means even at 100% conversion you will only get 120W, no matter the marketing claims of that device.
I can’t imagine his laptop will really burn 200W most of the time, but as my work laptop is power hungry as well, I can verify the built in inverter is not up to the task.
You either need an inverter you can run off the battery with direct wiring, or some sort of Jackery type solution. If he’s really burning 200 W, you are going to want at least a medium size one with 500w inverter and 500WH capacity. In a perfect woeld it will have a DC input for charging that you can then run off one of the 12v ports to keep it charged while driving. It will possibly run at a deficit while driving, but as long as it’s always getting some help from the truck, it will probably be fine.