Theft and fraud on a large scale?
The woman is claiming a 25% discount on her council tax, and even that may be legal, depending on her son's circumstances, which we don't know.
I think there is a lot of hysteria on this thread. If the OP's husband is paying his daughter some extra money, that is kind of him, and IMO perfectly understandable - I would do the same. It is not illegal, and she is under no obligation to declare a gift from a parent. Helping our children when they need us is What Parents Do.
The rest (she runs a car, gets her hair done etc) sounds like jealousy to me. If the woman has been working for years before the redundancy, presumably she will have saved some money for a rainy day, and she has been given a payout (again, perfectly legal - in fact a legal requirement). This is the rainy day. What is wrong with her spending her own money on running a car and getting her hair done? She will want to look decent if she gets an interview, and may well need a car for her work when she gets it.
The 'good clothes' she has were presumably bought while she was earning. If she sold them, she would get a pittance, and would then have to replace them with new ones when she finds a job. What do those who condemn her think she should wear? Should she buy special 'Universal Credit' clothes, and save the 'good' ones for when she stops claiming? If so, where should she get the money to buy them?
The fact that the son has 'a good job in the city' is irrelevant, too. Why mention it, if not to imply that, as with the 'good clothes' and the car, they are in some way undeserving?
Yes, claiming the discount on the council tax is wrong, if the son is living there as his sole residence, and not just staying with his mum for a couple of weeks. But 'theft and fraud on a large scale' is the sort of thing that companies such as Amazon commit when they defraud the taxpayer of millions of pounds. This does not come close, and if the OP betrays the confidence of her step-daughter over this, she is likely to cause a family rift that will never be healed.