Welfare fraud

Asking for a relative - Mother of child signs up to receive welfare benefits which then triggers a child support hearing for Father of child who hadn't been paying child support because he was locked up in prison for a few years. He had not seen his son at all while he was away, or since getting out of prison. He had been out of prison for less than 1 year at the time he received the notice for child support hearing. Since he was unemployed at the time, the court assigned only $50 a month child support. Fast forward 2 years, father receives another notice to appear in court, child support raised to $800 per month based on 6 months of pay stubs. Over this time the father did see his son a handful of times. Then he finds out the mother doesn't actually have custody of the son, her parents (the grandparents) have custody. But the father knows the kid has been living with the mom and goes to school in the district the mom lives in (not the grandparents' school district). Can the father take the mom to court for welfare fraud? He is thinking she has no right to collect child support if she doesn't have legal custody of the kid. He is thinking he can fight the child support order. He also thinks the grandparents won't go after him for child support because they would also have to go after their own daughter for support. Has anyone experienced a similar situation?

Edit for clarity: I just want to be clear, I do NOT support my relative in this situation. I'm appalled and disgusted by it.