I appreciate and note your advice about installing the driver on both iMacs, physically connecting the printer to both and deleting/re-adding the printer etc. However, because both SWMBO and myself can still print normally after the Apple update without having performed any of these routines, I haven't followed it yet. I'll keep it in reserve!
Looks like I'm gonna have to make use of this reserve because the wretched software update message has started to reappear! I had 10 day's grace after installing the Apple sourced update but now I'm back to square one. Or should it be square root.
When SWMBO's university assignment is finished (next week), I'll delete and re-add the printer on both iMacs. Next week because the house will reverberate with curses and abuse if this action somehow stuffs up printing completely.
