Hi, I'm Sudipto. Welcome to JustAnswer. I'm reviewing your question now, and will post back with your reply ASAP
As you have used the backup drive to restore the data, it means the driver for the older version of Mac got installed. Please open the link below then, download the HP utility and run it then, follow the onscreen instructions to reinstall the printer.
Hi, my name is ***** ***** welcome to Just Answer.com. I want to try and help you with your question.
Sounds like 2 things might be happening.
First in order to get your old info from your old mac to your new one, The easiest way is to use "Migration Assistant" that is built into the OS. Here is more on how to do this:
When you mentioned that you used a "back-up" drive, do you mean you backed up all your individual files to an external HardDrive or flash Drive?
2nd, it sounds like you would like to get your HP Office Jet Pro 8600 working again. After, I can make sure you have all your old data on your new mac we can proceed to fix your printer issue. Please let me know the info above and when you are ready to proceed.
If you need help with the migration or have any questions please don't hesitate to ask.