Renewing a PIP claim made under DS1500 vs making a new claim

Hoping someone here can point me to some legislation as I can’t seem to find anything myself…

I have a client who claimed PIP under DS1500 rules two years ago. The DS1500 was awarded due to severe COPD. Happily the client has outlived her prognosis and is currently stable. However she is now facing the end of her PIP claim which will happen in June.

We are not sure whether she would qualify for a new DS1500 although I have asked her to explore this with her doctor.

The DWP are insisting that she has to make a new claim for PIP rather than have a review. They are adamant that this is ‘the rules’ when someone outlives a DS1500. I am sure this is not correct as I’ve witnessed multiple people who originally claimed PIP on DS1500s get reviews when their claims come to an end just as ordinary PIP claimants do.. however I need some actual legislation to quote at them and I can’t actually find anything about the rules regarding what happens when someone needs a PIP review for a claim originally done under special rules. Can anyone help me? (Or indeed tell me I’m wrong and the client does need to make a new claim in which case I will have to start this as soon as possible.)

The PIP award is limited to 3 years under a DS1500 (see para 2079 of ADM). Normally what should happen is the DWP contact the clt 3 months before the end of the award to renew their claim.  Reg 33(2) UC, PIP, JSA & ESA (C&P) Regs give provision for the claim to be renewed up to 6 months before the award ends.
I find if another DS1500 is appropriate the 3 month period is enough to keep benefit continuously in payment following the three year award, but if DS1500 is no longer appropriate there can be a period where no payment is made until the full assessment process is completed, but payment will be backdated as long as the claim is made prior to the previous award finishes.