He needs to find his son and know why the mother didn't tell him she was moving out of town and when and where, also without a contact number? He hasn't seen him since two weeks before Christmas and talked to him since he had surgery in January! How do he get answers and be united with his son? That's his main focus, finding his son and knowing he's doing okay.
Has your fiancé established his status as the child's legal father. I would say that he needs to hire a lawyer to investigate this, and file an appropriate action to reunite him with his son.
Family Law Attorney
When exactly did the mother move out of state? If it has been less than 6 months, then she has not officially had a chance to establish residency in another state, and you can proceed with a civil action here in Georgia. If it has been more than 6 months, then you will have to proceed with an action in the county of her current residence which is out of state.
Was the child born in wedlock or out of wedlock? If the child was born out of wedlock, did your fiance ever legitimate the child, and obtain formal visitation rights through a court proceeding? If not, then your fiance needs to file a Petition for Legitimation, Custody and Child Support, so that he can get formal rights to his son, and establish a parenting plan where he will get visitation time. I strongly suggest that you or your fiance contact an attorney as soon as possible and provide some answers to these questions.
Some attorneys, like those at my office, even offer free initial consultations, so that you can get an idea of what your best options are, and the costs involved.