This article also answers:


I don't see the Push to Live Site option for my email notifications. Why?

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Yes, there is. This option is separately available for each email notification. 


Just navigate to Settings >> Email Notifications (under Customer-facing essentials). Now click on the email notification you'd like to copy and hit the Push to LIVE Site option. Here's a screenshot. 



Note: This option will be visible only if your TEST site has a LIVE version. 


More information on this here.