g5 15 5590 gtx 1650 with 240hz monitor

My son has a  a three-year old G5 gaming laptop with the Nvidia GTX 1650 graphics card feeding a 144hz Acer gaming monitor. He's asked for an upgrade to a 240hz monitor for Christmas, but before spending the money I'd like to know if that'll work. Even now he's only operating at 60hz or 120hz for some reason (the monitor is set up to tell him the refresh rate in the top corner), so if that's a limitation of the laptop, is a 240hz monitor going to be a waste of money?