In order to send emails via Elastic Email servers while using Mautic software - you will need to properly configure your Mautic.
Navigate to Email Settings under Configuration panel inside Mautic Automation Software.
To send your emails, use following settings :
Service to Send Mail Through: Other SMTP Server
SMTP Host: smtp.elasticemail.com
SMTP Port: 2525
SMTP Encryption Type: None / SSL / TLS
SMTP Authentication Mode: Login
Username for selected email service: Use your Elastic Email API Key
Password for the selected email service: Leave empty for no change
Tip: You may need to use your API key as both your username and password.
Alternative Settings - please use these settings if your port 2525 is closed and you cannot connect via it :
SMTP Port: 25 or 465 or 587