Brother’s service is free. Pretty sure HP’s is as well. He will have to use his phone to receive through an app, but should be able to send if he has one of the later models and it’s got access to the web through his router.
It sure sounds like HP is running some kind of automagic port on the web for the purpose of putting out faxes. The challenge I see is how HP keeps everyone and their uncle and aunt from bombarding that port.