Is it permissible to pay money inherited from a forbidden source as a bribe to reinstate a dismissed brother to his job, or must it be given as charity and another amount paid?

There is no impediment to paying a sum of money inherited from illicit (haram) sources to someone who can reinstate your brother to his job from which he was unjustly dismissed, if your brother does not possess the means to reclaim his right, and if he is in need of the job.