What is the core purpose of Management Letter ?

I can agree with the following answers. I can add that management letter should include recommendations for improvement. This is the core element.

A management letter is an auditor's letter addressed to the client.  It is a letter written by company management that confirms the accuracy of an audit. An audit is an examination and verification of a company's financial and accounting records and supporting documents presented by a professional, such as a certified public accountant.

At the completion of the audit program the auditors provide  Management letter which contain relevant information about accounting and management issues in the entity. The review of these letter will help the management to strengthen its internal control as it contains identified deficiencies in the system in general, mainly the avenues of inappropriate access to information that it to be handled in a restricted way. The recommendations provide helpful insight over many issues.

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it is a statement issued in a form letter, prepared and signed by the organization's senior management, addressed to the external auditors, per which, the organization attests the accuracy of all its end of period financial statements, that has already been submitted to the auditors for their professional audit.

A management representation letter is a form letter written by a company's external auditors, which is signed by senior company management. The letter attests to the accuracy of the financial statements that the company has submitted to the auditors for their analysis.

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I. Support the answer given by colleague Mohammed Asim 

It's a lettere from the external auditors to the company management including their notes and observations on certain matters

A management letter is an auditor's letter addressed to the client, according to Allbusiness. It is a letter written by company management that confirms the accuracy of an audit. An audit is an examination and verification of a company's financial and accounting records and supporting documents presented by a professional, such as a certified public accountant.

A management letter identifies issues not required to be disclosed in the annual financial report, but represents the auditors concerns and suggestions noted during auditing." It includes the public accountant's conclusions concerning the company's accounting policies and procedures, internal controls and operating policies. It confirms that all the information enclosed within the company's financial statements is true and accurate and that all the required information has been disclosed. An evaluation is made of the present system, pointing out problem areas. Recommendations for improvement are cited. An audit is an IRS assessment of an individual or corporation's tax return to verify its accuracy. There are three types of audits: correspondence audits (the IRS mails a request for additional information), office audits (an interview is conducted at a local IRS office), and field audits (an interview is conducted at a taxpayer's place of business for a corporate tax return).

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To Prepare management letter to ou clients

A management letter identifies issues not required to be disclosed in the annual financial report, but represents the auditors concerns and suggestions noted during auditing." It includes the public accountant's conclusions concerning the company's accounting policies and procedures, internal controls and operating policies. It confirms that all the information enclosed within the company's financial statements is true and accurate and that all the required information has been disclosed. An evaluation is made of the present system, pointing out problem areas. Recommendations for improvement are cited