When a Case is closed, it will trigger an Apex class to send an email with the Case details. However, when someone replies to the email, it will go to the Case Owner's work Gmail instead of back to the same Case using the Email-To-Case feature that is already set up and working properly.
I even included the Case Thread Id in the Apex Class and I see it in the email body being sent. 

How can I make sure the replied email arrives back in the Case that triggers the Apex Class?