Talked to AT&T - they knew all about my problem of the iPhone thinking it sent the e-mail but nobody gets them
They had me delete my e-mail account on the iPhone and then Add a new account - it required two button touches and ten seconds to accomplish
Fixed the problem!
AT&T says something happens to my account settings in the iPhone - they all look correct but the iPhone does not handle the send correctly. Deleting and Adding fixes it.
ATT said this is an old problem that they and Apple have often discussed but Apple will not acknowledge it and will not provide the Delete/Add fix to their tech support menus so when a customer like me calls Apple Support they are not told about the easy and quick fix
The more I deal with the iPhone - the more I am impressed with the Arrogance of Apple