iphone 6S broken unauthorized part

I purchased a new iPhone for my daughter at the Apple store on Broadway in the Upper West Side on July 9, 2016. Two months later, the phone overheated and could not be turned back on.

My daughter brought the phone to the Genius bar at the same store where the phone was purchased. The phone was sent out for repairs and was deemed unrepairable due to an unauthorized part. No one has put any parts into this phone.

Apple is unwilling to explain any further why they will not honor the phone's warranty or the additional AppleCare that I also purchased. They refused to provide any information about the case in writing and have stated that my only option is to purchase a new phone for $600.

The phone has been returned to the store.

Is there anything I can do to have Apple honor the warranty?