Income becoming capital

Ongoing UC appeal after it was disallowed due to client going over the upper limit. All complicated by Debt Management making an erroneous payment of over £4000 which was then counted as her capital. DWP arguing that the erroneous payment is recoverable and can therefore ignore it (have then gone on to use a different figure in their calcuation..).

It’s possible, ignoring the correct amount of the erroneous payment, that her capital was never actually over £16,000 at any point.

Just wanted to check how the monthly payment of UC and the 4 weekly payment of PIP are treated. Definitely income when paid. Do they then count towards her capital after the end of the AP following the one in which they were paid? I think that’s what the ADM is saying.

Also how do they work out what out of which payments has been spent and what is left to become part of capital?