Is it permissible to borrow from someone who obtained an interest-based loan to establish a private project, provided that he repays his debt to the bank, in order to avoid the sin of dealing with usury, or not?

What your sister's husband did by borrowing with interest is forbidden and a great sin, and he must repent sincerely. It is permissible to borrow a good loan from him, and his possession of the money borrowed with interest, despite the sin, does not prevent the validity of the loan. It is recommended for him to pay off the remaining usurious debt to the bank at once, to reduce the interest and clear his liability.