Messages sent from email to a phone have to use what is called the "SMS Gateway", which you used in your self test. In my Android phone I can reply to those messages back to email, and reply to that back to the phone messaging.
I don't have the ability with my Android phone to block sent text messages that come from an email address, only from a phone number or an SMS Gateway address. There is a difference in how an iPhone handles text messages, so I don't know what all you can do. Android phones used to have a feature to block all messages except those in your contact list, but mine does not have this.
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