Is the surplus amount mistakenly paid to an employee considered unlawful money, and what should she do with this money, and is it permissible for her to donate it to her poor brother to help him get married?

The amount of money disbursed to you by mistake cannot be owned by you and must be returned to the entity that disbursed it, based on the hadith (definition), "On the hand is what it took until it fulfills it." It is not permissible to donate it as long as the responsible entity exists.

If it is possible to return the money without harm to the employee, by placing it in an envelope and giving it to the treasurer or manager, informing them that it reached someone by mistake without their knowledge.

If that is not possible, then returning it is obligatory even if the employee is harmed, because fulfilling the obligation (returning the money to its owner) takes precedence over harm to the employee. An example of this is discrediting witnesses, despite the harm it causes them. Al-'Izz ibn 'Abd al-Salam said: "Discrediting witnesses before judges involves the harm of revealing their secrets; however, it is obligatory because the interest and preservation of rights concerning blood, property, honor, chastity, lineage, and all other rights are more encompassing and greater."

However, if returning it is impossible, the money should be spent on general Muslim interests, such as donating it to the poor. It is permissible to give it to your brother if he is poor.