... it does not appear in the Applications folder along with the software for the 8630.
It's a print driver NOT an application, so depending on the device it may not have additional software.
... I still cannot get the printer to appear in the printer preferences list.
Where is this "printer preferences list" you mention?
Anyway, you may need to add the printer (again, if you had it before).
Be sure your printer is ON.
Launch System Preferences (from Apple menu or your Dock).
Click on the Print & Scan icon
In the left panel, if your HP 8500 printer is listed, try double clicking on the title as it might ask to locate the new driver. If nothing happens, then click once on the title and then click the minus (–) button below to remove it from the list.
Afterwards, click the plus ( + ) button and select "Add a printer or scanner".
In the Add window, the Default icon will be highlighted with a listing of found printers below. Select your HP 8500 printer and let if find the correct driver, which will show next to "Use:" (You can change that by clicking on the pop down bar and choosing a different driver.) Finally, click the Add button.
Also see instructions from HP steps #3 onward.
If the problem persists, try rebooting you computers, launch Disk Utility and run Repair Disk Permissions.
HTH