Apple bought CUPs in 2002 so if you're wife's Mac is not a relic, it should be fairly easy. The other unknown is the Printer Language used by the 12 year old HP printer.
If
Postscript - you should be good to go for basic printing
If
PCLx ->
Installing ghostscript on MacOS
If ZjStream wire protocol ->
Installing HP Color Laserjet drivers - Apple
On my Brother HL-5450 a firmware update enabled the universal print everywhere driver but at the expense of some printing capabilities. I ended up reverting firmware.