What is the ruling on a man remaining with this woman in the same house after his 'Aqd (marriage contract) to her was merely ceremonial (sūriyan) and he divorced her on the wedding night, knowing that she stole his money for him to marry her, and that he agreed with her on divorce after a period for her to return the stolen money?

Marriage is a great ritual, and it is not permissible to use it as a means to achieve material gains. Your brother erred by agreeing to a fake marriage.

If the marriage was invalid (did not meet the conditions), then it is not permissible for him to live with her, because she is a stranger to him.

If the marriage was valid and then a divorce occurred, then if she is still within her waiting period (iddah), there is no harm in them remaining together. However, if her waiting period has ended, then it is not permissible for them to remain in one house unless there is a mahram present, or each of them has separate accommodations.

Your brother must repent and cut off any unlawful relationship, and seek lawful ways to recover his money that do not violate Islamic law.