Is it permissible for a brother to offer the vowed charity on behalf of his brother if the one who made the vow is not well-off?

It is permissible for your brother to act on your behalf in giving the sadaqah (charity) that you vowed, from his own money, and by that the vow is fulfilled. Financial obligations to Allah, such as sadaqat and expiations, permit deputization on behalf of others, whether the obligated person is able or not, and whether they are alive or deceased. However, payment on behalf of a living person is not permissible except with their permission, whereas for a deceased person, permission is not a condition.