Problems after changing Apple ID primary mail address
I just bought a brand new iPhone 6 Plus from Telecom. Few months ago, when I left my former company I was using a 4S, which I left with them. Before I left, I changed the primary email address of my Apple ID to a personal one, used the old phone with this Apple ID until I left it with my old company. Now I got the mentioned new iPhone, and did the activation and could rebuilt from the backup properly from the the iTunes back-up of the old 4S. Works well. However, I can use the Apple ID with iTunes, but I could not connect to the iCloud as it shows the old primary email address in the iCloud Settings and did not accept the password which was not changed at all. Since the password is not accepted I could not sign out and even could not delete the new iPhone as I can not switch off the iPhone tracking service anymore...
Any suggestions?
iPhone 6 Plus, iOS 8.1.3