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Unbelievable !

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They do transfer ESAs again now, in fact it is blotted all over it. You are in fine shape but you need to get the ball rolling on the transfer. The seller needs to quickly complete some written requests, etc. This is almost the same as most any other brands of cars for extended warranties added later. You can head into mytesla section to read the full thing but here is the transfer/initiating a transfer portion directly pulled out below:

Transfer and Cancellation by Customer

  1. You may transfer this Vehicle ESA to a different private owner of the same Vehicle or, based upon the calculation specified in Section J(2)(a) through (c) below, as a credit applied to the purchase of a new Vehicle ESA for a new or Certified Pre-Owned (CPO) Tesla vehicle purchased by You, provided that you contact Tesla prior to any such transfer or purchase and submit the following:
    • A written request for Tesla to transfer this Vehicle ESA to the new owner or apply it as a credit to the purchase of a new Vehicle ESA for Your purchase of a new or CPO Tesla vehicle.

    • A copy of documentation evidencing (1) change of ownership and mileage at date of sale or (2) the purchase agreement (e.g., Motor Vehicle Purchase Agreement) for the purchase of a new or CPO Tesla vehicle.

    • Payment of a $100 transfer fee for a transfer to a new owner of the Vehicle.

    • Written documentation verifying all maintenance requirements have been met for the Vehicle during the

      Agreement Period for this Vehicle ESA.

      The following conditions are required for the valid transfer of this Vehicle ESA:
      • The Vehicle is subject to inspection by Tesla.
      • Transfer must take place within 30 days of change of ownership or at least 10 days prior to the delivery of a new

      or CPO Tesla vehicle.
      • You may not transfer this Vehicle ESA to a vehicle dealer or to the customer of a vehicle dealer. • All remaining underlying warranties and documentation must be transferred to the new owner.
 
From...

Service plans

which is their NEW wordage:

"
Can I transfer my Tesla Service Plan or Extended Service to the new owner if I sell my Tesla vehicle?

Yes, you can transfer the unused portion of your Tesla Service Plan or Extended Service Agreement with the sale of your Tesla. In addition, we’re going to take this opportunity to go one step further: Tesla owners can transfer the unused value of your Extended Service Agreement towards an Extended Service Agreement for a new Tesla Model S or Model X. Please refer to the Terms and Conditions for your Tesla Service Plan or Extended Service for more information. You can view these Terms and Conditions after logging into your Tesla account. Click on “Services Sign Up” and following the appropriate link for your chosen plan."

So either Tesla is violating their own policies. There was another blog after the recent controversial interpretation of the ESA wording where Tesla re-affirmed that the ESA would continue to be transferrable.

Of course that was taken with a grain of salt since Tesla hasn't yet fixed the actual contract wording.

Good to know. Transferable service plans are what I would expect from Tesla!