Insurance through the state...

My husband was on child support, but then him and his ex worked out an agreement and as of court today it’s been terminated. Only thing is since his child was on child support she got covered through the state for insurance. Her mom has insurance through her job but the child is not on it. My husband does not have a job at the moment, and he is on Medicaid (insurance through the state). Can he put the child on his insurance instead of her going on with her mom?? He does not claim her as a dependent on taxes (someone said that he can’t because of that) and he is not on her birth certificate.

Edit: The mom would, but she just started a new job 2 weeks ago and she has to be working there for 3 months until she can get insurance.