Hi gowcameron, and welcome to TSG.
Have you confirmed that the video controller in your computer can support a 240 Hz refresh rate at your desired resolution through the HDMI output port? If it can't handle it, then any kind of basic HDMI to DP converter won't help you get a true 240 Hz picture refresh rate.
Have you confirmed that the video controller in your computer can support a 240 Hz refresh rate at your desired resolution through the HDMI output port? If it can't handle it, then any kind of basic HDMI to DP converter won't help you get a true 240 Hz picture refresh rate.