Cannot access "ICloud" on new 5s

[Slicktype]

So my fiancé just received her new 5s (gold) and for some strange reason her icloud is setup as ########@mail.com.
She had the same issue on her Ipad a while back but I forgot how I fixed it. Her Icloud is supposed to read "@gmail.com" and not "@.mail.com. She made a mistake setting up hee Icloud a few years back and it has been an issue on every new device as this keeps happening when she restored her"new" devices from back up.
I had her go to apple.com to change her password on this @mail.com account and it went through on the site but she still cannot access the ICloud with her new password.
Is there a way to "Delete" the iCloud account on her phone without a password ?.
This is very frustrating as the only thing she would like to do at the moment is turn on "AirDrop".

Thanks !
JP

 

[AlliFlowers]

Has she tried logging out of iCloud on the device?

 

[Slicktype]

Has she tried logging out of iCloud on the device?

Yes..... Nothing works !. When she originally created the @mail.com account, she instantly changed it to @gmail.com "But", for some weird reason every time she buys a new apple device and restores it from "ITunes" it ---always---- has the @mail.com account on the new device and not @gmail.com.
Very strange and frustrating !.

 

[AlliFlowers]

What if she doesn't restore from iTunes?

 

[Slicktype]

She does not want to start fresh. She wants photos, music, texts etc.... To remain on her new phone.
I tried to back up from The cloud (not using ITunes) and it will not let me as it asks for a password for the @mail.com account. She had the same password for the @mail.com acc as she did for the @gmail.com acc.
Not sure what to do ?.
Any suggestions ?
Thx