Hi,
The Automatic sending does not work with an expired license. Your customer is probably adding emails to the queue and then starting the sending manually using the "Send now" option in the queue.
In case your customer has the reporting enabled you can check what was send. If it's disabled, please enable it and make sure it is set to Each time Acymailing is triggered. The log will show you what is sent.
You'll find it in Acymailing->Configuration->Queue Process. Scroll down and open the Advanced Configuration.
We strongly recommend to encourage your customer to buy a new subscription and update their Acymailing to the latest version. They are missing important updates and fixes, including important security vulnerability fixes.
Once they have updated their Acymailing visit the Security tab in the Acymailing Acymailing configuration, scroll down and open the Advanced configuration and click on the "Scan site files" button to check if the site has been comprimised.