Before taking this to court and spending time and legal fees, your son and the mother need to make some serious efforts to find the father. There are two reasons for this:
Firstly, if they can find the father then they can likely get him to agree to the adoption since father seems to have no relationship with the child and wants to get out of paying child support, I assume. That $3500 may have come from father recently filing income tax return(s) and the refund to him was diverted to Maintenance Enforcement.
Secondly, they will have to serve him for the court to process your son's application to adopt the child. An adoption will strip father of all his rights and obligations to the child and grant them to your son. Those orders aren't made lightly, and best attempts at service have to be made.
So your son and the mother should start with the obvious methods. Do computer searches for his name, ask his family and friends if they know where he is because there's stuff going on that he needs to be aware of. If that doesn't pan out, then let a private investigator take a crack at it. That shouldn't cost much, and they know ways of getting at information which the general public isn't privy to.
If the father literally cannot be located, then a motion to the court for the order that Maintenance Enforcement disclose any knowledge they have about him to the court may be necessary. Perhaps this recent payment has some details which will help to locate the guy.
There are a number of ways that this can proceed, but to answer you: yes, father needs to be served with the application to adopt and your son needs to start looking for the guy.
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