Any MHAAs here? Patient's name wrongly spelt on section papers

I have a client who has an unusual spelling to his first name. He has been sectioned and his first name has a spelling error consistently over all of his s3 paperwork. He checked and his NHS App also spelt his name spelt incorrectly which he has never noticed before. The name reads the same it was an issue of the wrong double letter. The MHA noticed immediately and put a file note with the section papers and scrutiny papers that this is an incorrect spelling and it is consistent throughout. My view is that this is sufficient for a s15 issue, but he wants to see all the documents corrected or a specific document indicating the error and amendment rather than a file note and believes he is now unlawfully detained. I do not know if there is a specific document, Ive read the COP and as far as Im concerned all is ok, however I am open to any view of any knowledgeable person