Just a warning note first: If anyone points you towards a site called Solvusoft.com, which appears to offer a driver for your printer, do NOT download from it. A bit of googling shows that the site is a well-known source of malware.
Your best chance of getting the transfer to work is to install the same driver back-up program on both machines. Back-up your driver(s) on the 'old' machine, copy the back-up file (via a USB stick) to the 'new' machine and then extract the back-up file there.
https://sourceforge.net/projects/drvback/