Hi @kate2021
Just to clarify?
You’ve installed the free WP Mail Logging plugin on your site. Within that email log plugin, you’re seeing the email for the customer report as having been successfully sent. That would be this email below from within your screenshot, would this be correct?

Image Link: https://cloudup.com/cmQ5b4vN91c
If this is the cae and you’re seeing the customer export email displayed within the WP Mail Log that indicates that your WordPress installation suscesfully sent the email to that email address.
If you have not received that emai, usually, this can be due to the emails which are sent by WordPress using your hosting web server being marked as spam. Those may either end up in a Junk/Spam folder or are being entirely filtered out by your email provider before reaching your inbox. This is a common issue with sites using the default hosting server based WordPress PHP method wp_mail()
for sending mail, which can have a number of issues.
https://docs.woocommerce.com/document/email-faq/
To solve this you could first get in touch with your host and see if they can fix any mail issues. I would then suggest setting up an account at one of the dedicated SMTP email providers listed within this document and using that to send all site emails as it’s a more robust email approach.
https://docs.woocommerce.com/document/email-faq/#section-7`