I am wondering why you would want to provide evidence of your side of the story after the case is completed? Why was this evidence not brought up during the trial? This may be something that you should talk to your attorney about.
As for writing a letter to the district judge, I would contact your attorney to get his advice on this matter. Your attorney knows more about your case and may have an opinion on why you should or shouldn't write a letter to the district judge.
*DISCLAIMER: The information provided is not intended as and does not constitute legal advice. The information provided does not create an attorney-client relationship