In theory, you have to "declare" the phone at the Customs Office when you leave Buenos Aires so that you can enter it back. They give you some kind of evidence

In theory, you have to "declare" the phone at the Customs Office when you leave Buenos Aires so that you can enter it back. They give you some kind of evidence that you can present when returning. Since I have never done it, I don't know if it is a sticker on the phone, or just an official form with the phone's serial number. In practice, your pockets are generally not checked when you enter the country.