Disability aspect of working tax credits

I have a question about the disability aspect of working tax credits.
My partner has just been approved for PIP, the lower rate of both components. He's received a letter today asking if he thinks he'd qualify for the disability aspect of WTC (being in receipt of WTC already).
Having read through the letter we think he'd qualify due to health problems in two respects:
1 - He has trouble with his joints and lifting and tipping a litre of water from a jug really is a struggle for him.
2 - He has problems with confusion and memory loss due to previous medical treatment.
He is under a rhumatologist and pain clinic for his joint issues.
He is under early investigations by a neurologist for his cognitive issues.

BUT...he doesn't have any formal diagnosis for either of the issues he has.

He's had scans for the joint problems showed no evidence of a visible arthritis condition being active at that time, but didn't discount it entirely and he's due an MRI brain scan at some point when all the pandemic calms down and he can actually get to the hospital.
So, I don't know what we can say to HMRC. Yes he has problems, that's why he applied for PIP, he's seen about half of all the depts in the hospital (it's like filling in a bingo card, we get a reserve car parking spot if we get a full row of dept visits), but no definite diagnosis to say "Yes, he has arthritis" etc.
Can we still apply for it without there being a name to what has been causing all his issues? Is there understanding and leeway in the system?

From what I've read it appears, like PIP, it's more about the affects rather than the diagnosis but he's very concerned about the lack of a label.

Thank you in advance.

Thank you for your help again Gordon!

Yes he was awarded 8 points for moving around so you answer has absolutely answered our question.
He's still quite nervous about not having a 'proper diagnosis' but your reply actually really points us in the right direction.