At what age does the mother’s custody of the child legally end, and is it possible for custody to be transferred to the divorcedfather

My son, an Egyptian national, was studying in Malaysia when he married a girl who is a refugee from Myanmar. His wife gave birth to a child and registered the birth without including the father’s name — meaning the child’s birth certificate does not list a father. She did this believing it would help her and the child obtain asylum in a European country or the United States.

Now, my son — the child’s father — wants to correct the situation by adding his name to the child’s birth certificate, but the mother refuses to cooperate and insists on keeping the child registered without a father.

My question to the lawyer is: how can you assist my son in having his name added to his child’s birth certificate? At what age does the mother’s custody of the child legally end, and is it possible for custody to be transferred to the father? He has already divorced her.