Is it permissible to take the cost of medical examinations from an illicitly obtained surplus amount, and donate the remainder to the needy family of the husband, instead of returning the full amount to the company after it became impossible to return it?

If the insurance is commercial, your brother-in-law is not permitted to benefit from it beyond the amount of premiums he paid. Any surplus must be spent on the welfare of Muslims. He is not permitted to give it to his family unless they are not his dependents or he is unable to provide for them.

However, if the insurance is Islamic, he is not permitted to take the amount exceeding the value of the invoices. He must inform the company of the true situation. He may benefit from the surplus amount only for examinations that the company requires, and the remainder must be returned to the company, even if indirectly. It is not permissible to give it as charity because it belongs to the company.