SSP with no medical evidence

I have a client H&W co, with the husband being the fee-earner and the wife genuinely working 15 hours a week on admin for the business and being paid between LEL and ET.  The wife became ill around Christmas time, and was quickly diagnosed with a terminal illness which left her unfit to work.  She was paid full pay for Jan and Feb and died in early March.

I advised the husband to get a sick note and then we could pay SSP.  He didn't actually get round to getting one.

Looking in to it further, I note that that SPM10415 states "It is up to employers to advise their employees what if any, evidence of incapacity they are required to produce."

Does this mean it is ok to reclaim the SSP element as she was clearly very ill, but no 'evidence' was obtained.  Presumably evidence of death would ward off any challenge to her being sick and entitled to SSP.

I believe we can claim back the SSP element despite lack of sick note but would like confirmation before I tell the client.

Thank you