We mark our orders as fulfilled on the orders page, however, we cannot identify which email template it is that we can edit the content. None of the provided templates in the communications settings match with what is being sent to our customers (we have been testing).
I would check each email template in Notifications page in the 3 sections related to shipping / fulfillment (Shipping, Local delivery / local pickup if applicable). If the email is coming from your store, it’s got to be one of those I would think.
If you have any apps connected that send emails, check those too.
The email may be different in preview mode in Notifications than it is in the actual email, depending on the contents of the email, so I would look at the code of the notification as well.
Another thing you can do:add some text to the Notifications email, then create a test order, then mark fulfilled and compare the email you got with the one you think it should be in Notifications (for example if your order gets fulfilled it’s probably the Shipping confirmation email). Once you identify the text you can verify it’s that email. With that test order, you can cancel fulfillment then fulfill again, giving you the opportunity to run some tests to see which it is.