One member went round and round with a similar issue until we found a note that that particular HP was not shareable. No one knew why.
There are DOZENS of reasons for printer shares to fail beyond that. From Account issues, to network settings and firewalls.
-> Frankly I wonder what people think about this mess.
My default printer network is seen by both my computer and my printer and I can connect from both.
When I try to print, the printer is shown as offline. I have done everything I can find on the Internet and the HP sight.
The network, by default, has no Internet connection, which should be okay.