I'm sorry but it's impossible to intelligently answer your question, even in a general way, as to "what kind of letter you should send." I suspect you mean what the content of that letter should be. Without knowing everything that happened in connection with the prior hearing, the basis of the employer's objection and continued appeal, and the "things you think should be said," your question can't be meaningfully answered. You should seek an in-person conference with a local attorney who handles labor & employment matters.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you (and am not your lawyer). Do feel free to call me at 404-668-3790 if you wish to discuss actual representation (the phone call also does not retain counsel; that requires an office visit and appropriate paperwork). In that a forum such as this provides me with limited details and doesn't allow me to review details and documents, it is possible that answers here, while meant to be helpful, may in some cases not be complete or accurate, and I highly recommend that you retain legal counsel rather than rely on the answers here. (You can also email my office at don@HawbakerLaw.) An email also does not retain my office, but can help you get an appointment set if you prefer not to call). I am happy to discuss possible representation with you. Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated my Law Office as a debt relief agency that can help people file bankruptcy.
Contact an attorney who is experienced in unemployment compensation and seek advice on whether or not you need counsel to represent you in this matter.