You should make sure that the "Sending Email" address in your Feedback Genius, for each message, matches either the email address that you use to log in to Seller Central, or is listed as an "Alternate Address" here. 

*Please note: Each marketplace can have a different list of "Alternate Address." Make sure you are checking each marketplace's "Alternate Address."

(If the link does not redirect properly, or you are trying to access Seller Central for a different Amazon marketplace, simply login to your Seller Central and click on Messages (top right). From the Links section on the right, click on Messaging Permissions.
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The "Sending Email" is the e-mail address that Feedback Genius will send messages from.

*Note: that this is NOT an email address that buyers will see.

When messages are sent through Amazon's Buyer-Seller Messaging system, it rewrites the message to include your Amazon store name and a cryptic looking email address i.e. asdfghjklmqwertyuip@marketplace.amazon.com.
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To update the "Sending Email", click on Automated Messages under Feedback Genius in the hamburger menu in the top left corner. From here, you can edit already created and saved messages by simply clicking on the pencil icon next to the email under the "Sending Email" column.

You will get a popup that will explain the importance of the "Sending Email," and you will need to click Save from the popup to ensure all your updates are saved correctly.