UC Overpayment calculation

Client was claiming UC as a single person and getting standard allowance and child element only - no housing costs. She then moved in with her partner and did not disclose this. Partner has significant (albeit fluctuating) income as well as rental obligations.

When calculating any overpayment, presumably a comparison is made between (a) the UC actually paid to the client and (b) the UC that the client and her partner would have received had they made a joint claim when she moved in with him. Is it clear that the latter amount will take account of the partner’s rent as well as his income?