<PAGE>   1

                                                                     EXHIBIT 4.6


The Warrant and the securities issuable upon exercise of this Warrant (the
"Securities") have not been registered under the Securities Act of 1933 (the
"Securities Act") or under any state securities or Blue Sky laws ("Blue Sky
Laws"). No transfer, sale, assignment, pledge, hypothecation or other
disposition of this Warrant or the Securities or any interest therein may be
made except (a) pursuant to an effective registration statement under the
Securities Act and any applicable Blue Sky Laws or (b) if the Company has been
furnished with both an opinion of counsel for the holder, which opinion and
counsel shall be reasonably satisfactory to the Company, to the effect that no
registration is required because of the availability of an exemption from
registration under the Securities Act and applicable Blue Sky Laws, and
assurances that the transfer, sale, assignment, pledge, hypothecation or other
disposition will be made only in compliance with the conditions of any such
registration or exemption.

                   WARRANT TO PURCHASE SHARES OF COMMON STOCK
                              OF POPMAIL.COM, INC.

WARRANT NO. FP-2                                                  Irving, Texas
                                                                  May 15, 2000


         This certifies that, for value received, FAIRVIEW PARTNERS, or its
successors or assigns (the "Holder") is entitled to purchase from Popmail.com,
Inc. (the "Company") Eighty Thousand (80,000) fully paid and nonassessable
shares (the "Shares") of the Company's Common Stock, $.01 par value (the "Common
Stock") at an exercise price of $2.50 per share (the "Exercise Price"), subject
to adjustment as herein provided. This Warrant may be exercised by Holder at any
time after the date hereof; provided that, Holder shall in no event have the
right to exercise this Warrant or any portion thereof later than August 24,
2004.

         This Warrant is subject to the following provisions, terms and
conditions:

         1.   Exercise of Warrant. The rights represented by this Warrant may be
exercised by the Holder, in whole or in part (but not as to a fractional share
of Common Stock), by the surrender of this Warrant (properly endorsed, if
required, at the Company's principal office in Irving, Texas, or such other
office or agency of the Company as the Company may designate by notice in
writing to the Holder at the address of such Holder appearing on the books of
the Company at any time within the period above named), and upon payment to it
by certified check, bank draft or cash of the purchase price for such Shares.
The Company agrees that the Shares so purchased shall have and are deemed to be
issued to the Holder as the record owner of such Shares as of the close of
business on the date on which this Warrant shall have been surrendered and
payment made for such Shares as aforesaid. Certificates for the Shares of Common
Stock so purchased shall be delivered to the Holder within a reasonable time,
not exceeding ten (10) days, after the rights represented by this Warrant shall
have been so exercised, and, unless this Warrant has expired, a new Warrant
representing the number of Shares, if any, with respect to which this Warrant
shall not then have been exercised shall also be delivered to the Holder within
such time. The Company may require that any such new Warrant or any certificate
for Shares purchased upon the exercise hereof bear a legend substantially
similar to that which is contained on the face of this Warrant.

         2.   Transferability of this Warrant. This Warrant is issued upon the
following terms, to which Holder consents and agrees:


<PAGE>   2


              a.   Until this Warrant is transferred on the books of the
         Company, the Company will treat the Holder of this Warrant registered
         as such on the books of the Company as the absolute owner hereof for
         all purposes without being affected by any notice to the contrary.

              b.   This Warrant may not be exercised, and this Warrant and
         the Shares underlying this Warrant shall not be transferable, except in
         compliance with all applicable state and federal securities laws,
         regulations and orders, and with all other applicable laws, regulations
         and orders.

              c.   The Warrant may not be transferred, and the Shares
         underlying this Warrant may not be transferred, without the Holder
         obtaining an opinion of counsel satisfactory in form and substance to
         the Company's counsel stating that the proposed transaction will not
         result in a prohibited transaction under the Securities Act of 1933, as
         amended ("Securities Act"), and applicable Blue Sky laws. By accepting
         this Warrant, the Holder agrees to act in accordance with any
         conditions reasonably imposed on such transfer by such opinion of
         counsel.

              d.   Neither this issuance of this Warrant nor the issuance of
         the Shares underlying this Warrant have been registered under the
         Securities Act.

         3.   Certain Covenants of the Company. The Company covenants and agrees
that all Shares which may be issued upon the exercise of the rights represented
by this Warrant, upon issuance and full payment for the Shares so purchased,
will be duly authorized and issued, fully paid and nonassessable and free from
all taxes, liens and charges with respect to the issue hereof, except those that
may be created by or imposed upon the Holder or its property, and without
limiting the generality of the foregoing, the Company covenants and agrees that
it will from time to time take all such actions as may be requisite to assure
that the par value per share of the Common Stock is at all times equal to or
less than the effective purchase price per share of the Common Stock issuable
pursuant to this Warrant. The Company further covenants and agrees that during
the period within which the rights represented by this Warrant may be exercised,
the Company will at all times have authorized and reserved free of preemptive or
other rights for the exclusive purpose of issue upon exercise of the purchase
rights evidenced by this Warrant, a sufficient number of shares of its Common
Stock to provide for the exercise of the rights represented by this Warrant.

         4.   Adjustment of Exercise Price and Number of Shares. The Exercise
Price and number of Shares are subject to the following adjustments:

              a.   Adjustment of Exercise Price for Stock Dividend, Stock Split
         or Stock Combination. In the event that (i) any dividends on any class
         of stock of the Company payable in Common Stock or securities
         convertible into or exercisable for Common Stock ("Common Stock
         Equivalents") shall be paid by the Company, (ii) the Company shall
         subdivide its then outstanding shares of Common Stock into a greater
         number of shares, or (iii) the Company shall combine its outstanding
         shares of Common Stock, by reclassification or otherwise, then, in any
         such event, the Exercise Price in effect immediately prior to such
         event shall (until adjusted again pursuant hereto) be adjusted
         immediately after such event to a price (calculated to the nearest full
         cent) determined by dividing (a) the number of shares of Common Stock
         outstanding immediately prior to such event, multiplied by the then
         existing Exercise Price, by (b) the total number of shares of Common
         Stock outstanding immediately after such event, and the resulting
         quotient shall be the adjusted Exercise Price per share. No adjustment
         of the Exercise Price




                                       2

<PAGE>   3


         shall be made if the amount of such adjustment shall be less than $.05
         per share, but in such case any adjustment that would otherwise be
         required then to be made shall be carried forward and shall be made at
         the time and together with the next subsequent adjustment which,
         together with any adjustment or adjustments so carried forward, shall
         amount to not less than $.05 per share.

              b.  Adjustment of Number of Shares Purchasable on Exercise of
         Warrants. Upon each adjustment of the Exercise Price pursuant to this
         Section, the Holder shall thereafter (until another such adjustment) be
         entitled to purchase at the adjusted Exercise Price the number of
         shares, calculated to the nearest full share, obtained by multiplying
         the number of shares specified in such Warrant (as adjusted as a result
         of all adjustments in the Exercise Price in effect prior to such
         adjustment) by the Exercise Price in effect prior to such adjustment
         and dividing the product so obtained by the adjusted Exercise Price.

              c.  Notice as to Adjustment. Upon any adjustment of the Exercise
         Price and any increase or decrease in the number of shares of Common
         Stock purchasable upon the exercise of the Warrant, then, and in each
         such case, the Company within thirty (30) days thereafter shall give
         written notice thereof, by first class mail, postage prepaid, addressed
         to each Holder as shown on the books of the Company, which notice shall
         state the adjusted Exercise Price and the increased or decreased number
         of shares purchasable upon the exercise of the Warrants, and shall set
         forth in reasonable detail the method of calculation and the facts upon
         which such calculation is based.

              d.  Effect of Reorganization, Reclassification, Merger, etc. If
         at any time while this Warrant is outstanding there should be (i) any
         capital reorganization of the capital stock of the Company (other than
         the issuance of any shares of Common Stock in subdivision of
         outstanding shares of Common Stock by reclassification or otherwise and
         other than a combination of shares provided for in Section 4(a)
         hereof), (ii) any consolidation or merger of the Company with another
         corporation, or any sale, conveyance, lease or other transfer by the
         Company of all or substantially all of its property to any other
         corporation, which is effected in such a manner that the holders of
         Common Stock shall be entitled to receive cash, stock, securities, or
         assets with respect to or in exchange for Common Stock, or (iii) any
         dividend or any other distribution upon any class of stock of the
         Company payable in stock of the Company of a different class, other
         securities of the Company, or other property of the Company (other than
         cash), then, as a part of such transaction, lawful provision shall be
         made so that Holder shall have the right thereafter to receive, upon
         the exercise hereof, the number of shares of stock or other securities
         or property of the Company, or of the successor corporation resulting
         from such consolidation or merger, or of the corporation to which the
         property of the Company has been sold, conveyed, leased or otherwise
         transferred, as the case may be, which the Holder would have been
         entitled to receive upon such capital reorganization, reclassification
         of capital stock, consolidation, merger, sale, conveyance, lease or
         other transfer, if this Warrant had been exercised immediately prior to
         such capital reorganization, reclassification of capital stock,
         consolidation, merger, sale, conveyance, lease or other transfer. In
         any such case, appropriate adjustments (as determined by the Board of
         Directors of the Company) shall be made in the application of the
         provisions set forth in this Warrant (including the adjustment of the
         Exercise Price and the number of Shares issuable upon the exercise of
         the Warrant) to the end that the provisions set forth herein shall
         thereafter be applicable, as near as reasonably may be, in relation to
         any shares or other property thereafter deliverable upon the exercise
         of the Warrant as if the Warrant had been exercised immediately






                                       3

<PAGE>   4





         prior to such capital reorganization, reclassification of capital
         stock, such consolidation, merger, sale, conveyance, lease or other
         transfer and the Holder had carried out the terms of the exchange as
         provided for by such capital reorganization, consolidation or merger.
         The Company shall not effect any such capital reorganization,
         consolidation, merger or transfer unless, upon or prior to the
         consummation thereof, the successor corporation or the corporation to
         which the property of the Company has been sold, conveyed, leased or
         otherwise transferred shall assume by written instrument the obligation
         to deliver to the Holder such shares of stock, securities, cash or
         property as in accordance with the foregoing provisions such Holder
         shall be entitled to purchase.

         5.   No Rights as Stockholders. This Warrant shall not entitle the
Holder as such to any voting rights or other rights as a stockholder of the
Company.

         6.   Registration Rights.

              a.   Piggyback Registration Rights. Provided that the Shares are
         not then included in a current registration statement of the Company,
         if the Company, at any time before the fifth anniversary of the
         issuance of this Warrant, shall file a registration statement with the
         Securities and Exchange Commission ("SEC") under the Securities Act of
         1933, as amended, for the purpose of registering shares of Common Stock
         for sale to the public, the Company shall give to the Holder at least
         twenty (20) days advance written notice of its intention to file such
         registration statement and Holder shall have the right to have included
         in such registration statement such number of the Shares as it shall
         designate to the Company within ten (10) days after the date of such
         notice, provided that the number of Shares to be included in such
         registration statement, when added to all the other shares to be
         included therein, does not exceed the number of shares which the
         Company and its underwriters, if any, reasonably fix for inclusion. If
         the number of Shares to be included in such registration statement is
         less than the total number of Shares which the Holder has requested to
         be included, then the Holder and other holders of shares of Common
         Stock or other securities of the Company entitled to include shares of
         Common Stock in such registration shall participate in the underwriting
         pro rata based upon the total number of shares of Common Stock
         requested to be registered by all of such holders. The Holder shall
         furnish the Company with such information as may be required in
         connection with such registration statement and will cooperate to cause
         such registration to become effective at the earliest practicable time.
         If the shares to which such registration relates are to be sold in an
         underwritten offering, the Holder, as a condition to the inclusion of
         the shares in the registration statement, shall agree that its Shares
         will be sold only as a part of such underwritten offering and at the
         price and upon the terms fixed by the Company and its underwriters,
         subject to the right of the Holder to withdraw the Shares therefrom.

              b.   Demand Registration Rights. On a one-time basis only, during
         the three year period commencing two years after the date of this
         Warrant, upon request by the Holder or Holders of a majority in
         interest of this Warrant, and of any Shares, the Company will promptly
         take all necessary steps to register or qualify, under the 1933 Act and
         the securities laws of such states as the holders may reasonably
         request, such number of Shares issued and to be issued upon conversion
         of the Warrants and shares of common stock of the Company




                                       4

<PAGE>   5


         owned at such time by such holders pursuant to the conversion of that
         certain $2,000,000 Senior Convertible Note issued as of the date of
         this Warrant requested by such holders in their request to the Company.
         The Company shall keep effective and maintain any registration,
         qualification, notification, or approval specified in this section for
         such period as may be reasonably necessary for such Holder or Holders
         of this Warrant and/or such Shares to dispose thereof and from time to
         time shall amend or supplement the prospectus used in connection
         therewith to the extent necessary in order to comply with applicable
         law.

         7.   Governing Law. This Warrant shall be governed by and construed in
accordance with the laws of the State of Minnesota.

         8.   Amendments and Waivers. The provisions of this Warrant may not be
amended, modified or supplemented, and waiver or consents to departures from the
provisions hereof may not be given, unless the Company agrees in writing and has
obtained the written consent of the Holder.

         9.   Notices. All notices or communications hereunder, except as herein
otherwise specifically provided, shall be in writing and if sent to the Holder
shall be mailed, delivered, or telefaxed and confirmed to the Holder at his or
her address set forth on the records of the Company; or if sent to the Company
shall be mailed, delivered, or telefaxed and confirmed to PopMail.com, Inc.,
1333 Corporate Drive, Suite 350, Irving, Texas 75038 or to such other address as
the Company or the Holder shall notify the other as provided in this Section.

        [The remainder of this page has been intentionally left blank.]



















                                       5

<PAGE>   6

         IN WITNESS WHEREOF, PopMail.com, Inc. has caused this Warrant to be
signed by its duly authorized officer in the date set forth above.

                                            POPMAIL.COM, INC.


                                            By
                                              ----------------------------------
                                            Its
                                               ---------------------------------







<PAGE>   7







                               SUBSCRIPTION FORM

         To be signed only upon exercise of Warrant.

         The undersigned, the holder of the within Warrant, hereby irrevocably
elects to exercise the purchase right represented by such Warrant for, and to
purchase thereunder,                      of the shares of Common Stock of
PopMail.com, Inc. (the "Shares") to which such Warrant relates and herewith
makes payment of $              therefor in cash, certified check or bank draft
and requests that a certificate evidencing the Shares be delivered to,
                               , the address for whom is set forth below the
signature of the undersigned:

Dated:
      --------------------

                                 --------------------------------------------
                                 (Signature)


                                 --------------------------------------------
                                 --------------------------------------------
                                 (Address)



                                      * * *



                                 ASSIGNMENT FORM

        To be signed only upon authorized transfer of Warrant.

        FOR VALUE RECEIVED, the undersigned hereby sells, assigns, and transfers
unto                               the right to purchase shares of Common Stock
of PopMail.com, Inc. to which the within Warrant relates and appoints
attorney, to transfer said right on the books of                with full power
of substitution in the premises.

Dated:
      --------------------


                                --------------------------------------------
                                (Signature)


                                --------------------------------------------
                                --------------------------------------------
                                (Address)












                                       7