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When about him moving away from her, do you mean what if he moved away from the country that the child is in?
So are you asking about whether he could not live with the mother and still have custody or access to the child?
Whether the child is born outside of marriage or not does not matter from a legal perspective. He has the same rights to custody and access as any other parent would have. He also has the same obligations to support the child.
So he can seek sole or joint custody or access though it would be very difficult to gain sole custody of an infant.
His next step should be to consult with a family lawyer face to face in your city.
Does that help as as starting point?