If mom is in Ohio... Ohio can determine that he has abandoned the child. Has he been paying child support? Can I state that Ohio has proper jurisdiction? No.. but in Probate court if mom is remarried, yes, they would... so mom could pursue a stepparent adoption and dad's consent would NOT be necessary. IF she is in Ohio and remarried.Sorry, Red. Parental rights don't go away just because parents decide for whatever reason not to exercise visitation. Your information is as bad as anybody else's in the thread.
The only clear thing is he needs to be talking to an attorney that specializes in these things, to determine what exactly the situation (is there an obligation not to move with or without notice to the state/father and then what to do next.