GXT1000 Car charge voltage

Hi there, question regarding the Midland GXT1000 GMRS radio. The kit comes with a charger and a 110V wallwart that puts out 9V DC and a 12V car “cigarette lighter” cable. I measured the voltage, the car adaptor puts out 12V.

My question, can I power the radio charger directly from the car? Just a (fused) connector to the battery rather having to plug it in?

Voltages seem to match, I can’t see a reason why it won’t work. Asking the experts here first. Thanks!