If the extension doesn't work as expected (e.g. abandoned cart emails are not sent, quotes are not added to the queue), we'd recommend checking the module configurations following the instructions below. 

1. The abandoned carts are tracked within the campaigns. Please, make sure a campaign in Marketing → Abandoned Cart Email → Campaigns is created and configured:

2. Make sure the Cron is installed and running on the instance. Kindly refer to the following Magento guide to configure cron. Also, note that abandoned cart emails are being sent by Cron, and by default Cron sends emails once in 5 minutes. It means that every 5 minutes Cron checks whether there are emails to be sent and if so, it sends them.

3. In case cron is running, however, the emails are not sent kindly navigate to Amasty → Abandoned Cart Email → Configuration and check if Safe Mode is disabled: 

4. Additionally, please check that the created abandoned cart falls under the campaign conditions (Stores and Customer Groups, Conditions) and matches the Send Emails to Registered Customers Only and Send Emails to Newsletter Subscribers Only settings.

To check whether the created quote meets the conditions, you can check the Test tab in the Campaign created - if the record is there, the cart meets the campaign conditions:

5. If the website has multiple campaigns created on the instance, review the Trigger Campaign Only Once per Quote setting, if it is enabled, the email will be sent only for the one campaign with the highest priority: