UC/Tax Credits backpay following DLA Appeal decision

Hi
Can anyone help with this - DWP and HMRC are batting my client backwards and forwards?
Claimed UC in March 2020, had a DLA Appeal for her son pending which was heard in November 2020, he was awarded MRCare from 15/1/2019. 
Prior to the UC claim she was receiving Child Tax Credit at the ordinary rate for her son, the disability element stopped when his DLA stopped.
UC have (eventually) paid the disabled child element and taken off the benefit cap but are refusing to pay the extra client was due as Tax Credits (prior to her UC claim) for a disabled child - they are saying she must go to HMRC.
HMRC are saying she must get the extra off UC.
This has been going on for a while now - who should be paying the extra - all advice gratefully received.
Thanks

DWP can’t pay elements of UC for a period before you claimed it.

The tax credits awards can be revised by HMRC to account for the child’s disability subject to various other rules discussed here:
https://revenuebenefits.org.uk/tax-credits/guidance/how-do-tax-credits-work/making-a-claim/backdating

That’s great Elliot, thank you