Thank you for reaching out to us. We certainly want to make sure that you can see all of your message logs. Have you looked within iMessage under the sent option? Through your My Verizon you do have the option to view call/text logs. You can see more here: http://spr.ly/65878oBYJ.
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On the phone where the messages reside, go to the thread and open it as if you're going to send a message. You will need to slide from the right side of the screen to the left side of the screen to reveal the of each message.