Email Notifications Do Not Send to External Email Addresses
When running a workflow that is configured to send email notifications to external email accounts, such as Gmail, Hotmail etc., the workflow completes but emails notifications are not sent.
Confirm the issue occurs with the workflow in SharePoint Designer. Review the Exchange setup and ensure the external email accounts are being set. For more information on setting up a connector, seeCreate a Send connector to send mail to the Internetin Microsoft TechNet.