Is it permissible for a Muslim who vowed to give money in charity to his unemployed brother upon his promotion, to give this money in charity to another person or people after his brother succeeded in finding a job and before fulfilling the vow?

A conditional vow must be fulfilled when the condition upon which it is based is met. Regarding giving the vowed charity to someone other than a brother: Scholars have differed on whether a vow of charity to a specific person necessitates giving it to that person or not. The apparent view is that it does become designated. However, Ibn 'Abidin holds that in a conditional vow, neither the place nor the poor person is designated; rather, what is affected is expediting its fulfillment. Therefore, if the intention of giving the charity to your brother was not specifically designated, then it is permissible to give the vow to someone else. However, if you intended to give the charity to him due to his poverty, and then it became clear that he is not poor, your intention specifies the vow and obliges you to give it to a deserving poor person. If you did not have a specific intention, it is preferable to give it to your brother.