Paying off HB/CTS overpayment to reclaim benefits

Hopefully a quick query.  My client has recently been told he has a huge HB/CTS overpayment due to undeclared savings (and private pensions) and his HB/CTS has been stopped.  Can he pay back some or all of the overpayment in order to reclaim HB/CTS (in other words does the overpayment count as a debt that has to be repaid) or does deprivation of capital come into it?  The situation is more complicated than that but I just want to know if that is an option for him.

CIS/4315/2012 - http://www.osscsc.gov.uk/Aspx/view.aspx?id=4417 - just published last month discusses notional capital and repaying debt - summary will be in the caselaw section imminently…