Trade-in Iphone program in another country

Please note:

1. If you buy your phone in the US, iPhone warranty is NOT international
2. When you go back to Italy, should you have an issue with your phone, which requires service or replacement, you may not get any help in Italy
3. Apple does not accept international shipment, so you cannot send the phone to Apple in the US
4. You would have to get on a plane and bring the phone back to Apple
5. Apple sells phones regionally, you need to make absolutely certain a phone you purchase in the US will work properly in Italy
6. Any savings you might realize by buying a phone in US will be gone should you need service or replacement if you have to bring it back to the US
7. Buy your phone in the country you live and will use the phone to avoid any of this

Ciao!

They should accept it, I don't see why not. They will have you reset it so it shouldn't matter where it was bought.