Correction
I have found the problem with not getting email out on the IPhone 4S. It is with Optimum. I now remember this company did the same thing when I switched to a Blackberry two years ago.
The problem was Optimum was trying to wear me down into upgrading our service with them.
It took three phone calls to Optimum about the new IPhone's outgoing email problem. On the third call there are statements about not using them as my incoming email carrier (which has nothing to do with the outgoing mail that goes directly to them) , vague references to needing an upgrade, and then some casual statement about needing a password and user ID (gee, this is new news to us and the phone used for the last two years did not need one...but I get the need for increased security, so why weren't we told this on the first phone call! They wasted six hours of my day, and the time of agents at Verizon 2 times as we went back and forth on this).
It took really working the representative over until he agreed to tell me the new settings needed to get the outgoing email to work on the IPhone.
These folks also basically lied us out of a lower cost TV cable package that we were grandfathered into a few years ago. Be careful.
I wish other companies had the integrity that Apple has.