Not sure if you are trying to share the printer over a network, or just moving the usb cable between the two computers as needed.
Regardless, the printer model you specify, is that specifically a model 1500, or is it a 1500 series?
The reason I ask is that hp has an installer for ubuntu 12.04 for psc 1503, 1504, 1507, and 1508 models.
The above link indicates a
Should walk you through the setup.
Found this link from Ubuntu support that may help:
I apologize if you're already past all this.
As others have stated, if you're using Ubuntu and an open source backend driver exists for your printer, it's probably already installed. I always use the web-based interface (localhost:631) to configure it, but I believe Ubuntu also comes with a graphical configuration wizard that you'd probably favor over that.