Recently I ran into an issue trying to use non-HP ink cartridges in our HP OfficeJet Pro 7740.
I kept getting an error saying " Please install Genuine HP Ink Cartridges to ensure maximum quality"
With the help of our IT consultant, we found a Youtube video and instructions on how to install new (old, actually) firmware in order to be able to use third-party ink cartridges.
The instructions were horrendous and the video was even worse, so I took the liberty of creating a new set of instructions from the ground up. See the attached PDF document with embedded links to the firmware download page, as well as further reading for those interested in why this type of action is needed in the first place.