Can a mother make a life insurance claim on behalf of a minor child if they are the named beneficiary?

Probably. Check with the claims department of the insurance company. It would be better if a trust had been set up to receive the benefits on behalf of the minor. The Mother may have to go to court to get authorization to sign for the child. For more info see www.SteveShorr.com/life.htm and www.SteveShorr.com/estate.planning.htm