When setting up your NPS campaign you have different options in selecting who the NPS survey will come from via a field called "Send Message From".
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If you select "Account Owner" and the account that the end-user is associated with doesn't have an "Account Owner" then the NPS survey will not be sent.
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The email will be stored in the "Waiting for approval" folder on the Conversations module (See image below).

If you look in the top right hand corner of the conversation you will see a red triangle with a white exclamation mark and if you hover over it you will see the following error message: "Send error: Unable to identify send "accountOwner".
Please edit it and choose a valid sender.

Add an "Account Owner" to the account, locate the email in the "Waiting for approval" folder and select "Approve to be sent" (this is a tick on the email, see image below).