You need the hplib package.
But you don't find it in the Software Center if you serach for it by its name, you have to search for it by just typing hp and nothing else. (Strange but don't ask why.)
You also need the hplib-drivers package but that, I believe, is installed together with hplib.
Then install your HP printer via the settings utility:
Open SETTINGS, DEVICES, PRINTERS.
Click on UNLOCK top right, enter your admin password, click OK.
Connect your printer if it's not already connected, and turn it on.
Let SOLUS search for your printer, click ADD once it's found.
That should be it.
You can then adjust the settings of your printer to your needs.
