You may need to switch accounts. For instance, if you transfer the site to a new own. This is done through the General Settings screen.
To switch Site Mailer accounts:
- Go to WP Admin.

 - Navigate to Settings>Site Mailer.

 - Click General Settings.

 - Scroll down to the Account section.


 - Click the ellipses 
on the right hand side of the Account area.

Select Switch account.