I have an iPhone 5s and I too have the same problem. I was texting my mother and after the conversation was long finished (~40 minutes later) I got the same message that she had first sent me to start the conversation.
I've had this problem for about a month now; I've noticed it tends to happen the most if I turn my cellular data setting on after I have turned it off. When I turn on cellular data, I'll get a few messages that I have already recived. This isn't always the case though (the example I explained above was not after changing cellular settings)
I only got my iPhone in May of this year, and it's July now, so the phone is extremely new, and hardly considered used. It is also up to date on all the most recent software/firmware. Even after a good shut down on multiple occasions the problem still persists.
Any suggestions?
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Also @deggie,
Recieved messages don't specify a color for SMS or iMessage, that's only when you send a message. However a small indicator will say whether or not the message was sent via SMS or iMessage as exemplified below (at least I know this is the case for the iPhone 5s, I can't speak on behlaf of other iPhone Models)
