A friend of mine previously had nothing but a pc and one Gmail email address which I will call here "email@example.com". She then got first an iPhone and a little later an iPad and used "firstname.lastname@example.org" as her Apple ID. A couple of weeks ago she also got a MacBook as a replacement for her pc and is by now using only iOS and OS X devices. She is now also using iCloud on all devices for syncing her calendar and her contacts.
When she started to use MobileMe (there was no iCloud yet at that time) she had to create a me.com email address. Unfortunately she chose "email@example.com" and now she has "firstname.lastname@example.org" and "email@example.com" as email addresses in her iCloud account.
The only email address she wants to use is "firstname.lastname@example.org" and this email address is as IMAP account in Mail on her iPhone, her iPad and her MacBook. However, when she started to use iCloud she had (or at least thought she had) to add her weird and unwanted icloud.com email address to Mail on her iPhone (and later on her iPad) and therefore she used for quite a while unknowingly "email@example.com" when sending emails from her iPhone or her iPad and because of that she also receives many emails to this email address (which get forwarded automatically to her Gmail account).
The question now is whether (and how) it is possible to get rid of the unwanted iCloud.com address from iPhone and iPad so that a) whenever she replies on her iPhone or iPad or MacBook to an email that got send to the iCloud.com address (and forwarded to Gmail) and b) whenever she starts a new email on iPhone or iPad or MacBook automatically only the Gmail address is used as the sending address.
At the same time she, of course, would like to see all sent emails also in the Sent folder on all three devices.
Is this doable? Am I just not seeing the solution, or is this all somehow complicated?