If an iphone is linked to another Apple account, can it be added to another account?

A phone was given to my wife from my daughter and it was linked to her Apple account. My wife just purchased a new phone, but Att. Service center was not able to unlink the new phone from my daughter’s Apple account without losing all the contacts,etc. that were stored in the I-cloud. Is there a way to unlink the new phone from my daughters Apple account without losing info?