@OrchidBob - thanks for the detailed response. Years ago the pot fell over and the tops of both stems broke off. I don't think my mum was successful in getting them to grow, but we didn't know about leaving the cut piece to callus over for a week or two first at the time.
I am hoping to be able to transport this cactus to my new home over Christmas and then I'll be able to cut the healthy top section off and pot it up as you suggest. I'll have to check with my mum if she has cut the yellowing stem off yet (I asked her to do so if it continued to decline) and if not, to cut it back an inch or two above the previous break to expose a new eye.
