REPORT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

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

In planning and performing our audit of the financial statements of
Hatteras Core Alternatives TEI Institutional 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