You must either use the form "Mr ....." or the informal first name alone, but not both.
In this kind of communication, with no starting salutation, you do not put in either "yours faithfully" or "yours sincerely". Your signature followed by name, job title and department is all that is needed.
TO WHOM IT MAY CONCERN
It is with great pleasure that I write this letter to support Mr. Rachid Bou Mujahid.
I have known Mr Bou Mujahid since the Malik bookshop has been at AUB. He has always been helpful, cooperative and efficient. I have found him reliable and willing to do whatever is asked / required of him.
We very much hope that he will remain the contact person for AUB at the Makil bookshop.