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.
I’m not up on exactly how it works, but my Asus router similarly, allowing me to remotely access it by going through Asus web services using a similar phone app. The string created contains a unique Id that obviously routes the connection from my phone through Asus to my router at home. Kinda of like those static ip service providers, I’m assuming.
I set my 4 servers up similarly to have access from anywhere using RD and port forwarding without a dedicated IP.
I send directly to the printer over the wireless LAN, while I’m on the network. I normally keep the printer’s access to the WWW blocked. It’s easy enough to control what has access by using the router’s phone app - all wirelessly - no cables or phone lines.
Did I mention my 3D printers are also WIFI? LOL And 4 Alex Echos, not to mention numerous “smart devices”.
Since we’re talking hitech, Alex is cutting edge. Tell her to call someone, she knows who you are by your voice and connects to that person’s cell phone to look up the contact number then dials the number through that particular phone, all the while allowing you to converse through surround sound via a bluetooth connection to your home sound system and will interrupt to remind you of a pending appointment, dinner is ready, or you just received a fax! :)