Also, your file can be doble check at the DNM to see the real situation of it BECAUSE if you do not live with your child, you are going to get a deportation order. However, the SC ruled recently again the deportation of parents of argentine children even convicted for drug trafficking.
Don't scare him off with legal mambo-jambo. With the new rules as of today he can fly to AR without a problem with the documents he already has.