Is what the judge did permissible, in terms of the deception in the story of his second marriage that you mentioned, and does that fall within the scope of lying, cheating, and fraud?

A man's lie to his wife, claiming to negate a second marriage, is permissible. This is because marrying a second wife is originally permissible, and his lie aims to preserve the relationship and affection with his first wife. The Prophet, peace and blessings be upon him, permitted lying in three cases: war, reconciling people, and a man speaking to his wife or a woman to her husband. This is concerning matters of companionship and achieving affection between them, provided that no right is abrogated or anything taken that one is not entitled to.