I think if it is the small type in line cat I'd just throw one on for 30 quid, There is no doubt other problems but a cat would probably see it through the MOT .
If it only doing 3k a year it probably never gets hot so has probably got premature engine wear but also the cat has to put up with a cold rich mixture for most of it's life which wouldn't do it much good & these cats are crap, I bet it's already had at least one maybe two so far.
I'd check before & after cat with infared temp gun just to comfirm,fit a non genuine cat,explain to customer shes killed her car by only doing short runs,a new cat is just a mask & that due to above issues there is no warranty on cat,oh & sell car before next years mot.
We all know it's not the right way but it's the cheapest route & the car isn't worth chucking hundreds at or many hours testing.
Matt
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