REPORT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

To the Board of Directors and Partners of Hatteras Core Alternatives
TEI Fund, L.P.

In planning and performing our audit of the financial statements of
Hatteras Core Alternatives TEI Fund, L.P. (the "Fund") as of and for
the year ended March 31, 2020, in accordance with the standards of
the Public Company Accounting Oversight Board (United States), we
considered the Fund's internal control over financial reporting,
including controls over safeguarding securities, as a basis for
designing our auditing procedures for the purpose of expressing our
opinion on the financial statements and to comply with the requirements
of Form N-CEN, but not for the purpose of expressing an opinion on
the effectiveness of the Fund's internal control over financial
reporting.  Accordingly, we express no such opinion.

The management of the Fund is responsible for establishing and
maintaining effective internal control over financial reporting.
In fulfilling this responsibility, estimates and judgments by
management are required to assess the expected benefits and related
costs of controls.  A fund's internal control over financial reporting
is a process designed to provide reasonable assurance regarding the
reliability of financial reporting and the preparation of financial
statements for external purposes in accordance with generally
accepted accounting principles (GAAP).  A fund's internal control
over financial reporting includes those policies and procedures that
(1) pertain to the maintenance of records that, in reasonable detail,
accurately and fairly reflect the transactions and dispositions of
the assets of the fund; (2) provide reasonable assurance that
transactions are recorded as necessary to permit preparation of
financial statements in accordance with GAAP, and that receipts and
expenditures of the fund are being made only in accordance with
authorizations of management and directors of the fund; and (3)
provide reasonable assurance regarding prevention or timely detection
of unauthorized acquisition, use or disposition of a fund's assets
that could have a material effect on the financial statements.

Because of its inherent limitations, internal control over financial
reporting may not prevent or detect misstatements.  Also, projections
of any evaluation of effectiveness to future periods are subject to
the risk that controls may become inadequate because of changes in
conditions, or that the degree of compliance with the policies or
procedures may deteriorate.

A deficiency in internal control over financial reporting exists
when the design or operation of a control does not allow management
or employees, in the normal course of performing their assigned
functions, to prevent or detect misstatements on a timely basis.
A material weakness is a deficiency, or combination of deficiencies,
in internal control over financial reporting, such that there is a
reasonable possibility that a material misstatement of the Fund's
annual or interim financial statements will not be prevented or
detected on a timely basis.

Our consideration of the Fund's internal control over financial
reporting was for the limited purpose described in the first
paragraph and would not necessarily disclose all deficiencies in
internal control that might be material weaknesses under standards
established by the Public Company Accounting Oversight Board
(United States).  However, we noted no deficiencies in the Fund's
internal control over financial reporting and its operation,
including controls over safeguarding securities that we consider
to be a material weakness as defined above as of March 31, 2020.

This report is intended solely for the information and use of
management and the Board of Directors of the Fund and the Securities
and Exchange Commission and is not intended to be and should not be
used by anyone other than these specified parties.



COHEN & COMPANY, LTD.
Cleveland, Ohio
June 1, 2020