This is a serious problem. As someone with audio engineering background I can honestly say that probably only condenser microphones (like those big Yeti Blue youtubers use) are going to do the job. Contrary to a popular belief the dynamic ones, even if head mounted, aren't the best idea.

You can buy a cheap condenser mic from China for maybe 30 bucks. It'll be fine. You'll need an usb audio interface with a phantom power to run it (another maybe 50 bucks). Or go the easy route and buy an all-in-one usb condenser mic like Yeti. There are also cheaper options available I'm sure.

But! Before your friend is going to buy something ask him to tinker with his audio settings. Even the best mic isn't going to save you if you don't have a control over your audio workflow.

turn the volume up when this person talks?

The software noise cancels their voice because it's too soft -- there's nothing to turn up.