I think you can treat the partner as owning the capital whether or not it is in the partner’s name. Whilst possibly not being treated as a member of the household, he is still her partner (N.B: did the assessment of capital include the home?).
Presumably there has been a claim for a passport benefit? If it has been awarded then I think your hands are pretty much tied – I would suspect that this would have been investigated leaving you little or no room to make your own decision – I do not think you could use Hamilton to go against if there has been an investigation.
If not:
As far as the amount of capital is concerned has the settlement figure been paid? If not then I think that if the Court is satisfied with the figure you (and TS) should be as well – ask for proof where the capital has gone. I do not think you could use a notional figure – the main purpose of disposal would be to avoid the settlement rather than claiming CTB
If it has been paid I think it is just a matter of going through everything with a fine-tooth comb. Given past history I do believe that you can reasonably expect a higher standard of evidence than would normally be expected (although this would have to be limited ‘cos it was not your current claimant who was convicted). It is probably worth getting another experian check run. Also do a visit – if the standard of living seems way too high given the declared income you can probably make a decision on that basis, especially if you have evidence to suggest that your current claimant knew what was going on.