Supersessions and backdating: Any suggestions?

Not sure if this belongs here or in the ESA-related section. My client, who has very severe depression has been entitled to contribution-based ESA for a long time.  Her partner, who worked full-time, left in March 2019. From that time onwards she should have been entitled to an income-related top-up but it never occurred to her to inform the DWP. (bereavement, partner left, mental illness).  In the future she might be better on UC (although there may be mortgage interest payments to consider) but is there any way in which I could argue for backdating of the income-related ESA?