The first paragraph of any business or academic letter should tell the recipient why you are writing. In the case of writing on someone else's behalf, you should open with this fact at the start of the first paragraph. You should also make it clear that the person you are writing for has requested that you do this or has not requested it. Example openings:
I am writing to you on behalf of your client (your patient, your customer, etc.), Maria Marx, at her request. Ms. Marx wishes to inform you (request, etc.) that...
I am writing to you on behalf of your client, Maria Marx, because I feel that her situation (case, treatment, etc.) should be addressed. I understand that Ms. Marx purchased (visited you for, attended your, etc.) on...
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