The proper way to address a judge is: "Your Honor" In a letter you use the salutation: To the Honorable [name of the judge], District Court Judge. You may want to contact your brother's attorney concerning the best way to present the letter to the Judge.
The information that I am providing is general information based on my understanding of your question. You cannot and should not rely on this general advice in making legal decisions. There may be important information that you did not include in your question that could drastically change the advice an attorney that was fully informed would give you. I am not your attorney. My response does not create an attorney client relationship.