The Verdict: Clear Path
Naturalising abroad did not end Greek nationality, so there is probably nothing to reacquire. Take our Citizenship by Descent quiz to check the line, then file for a determination of Greek citizenship.
Article 16 of the Citizenship Code, and article 23 of the 1955 Code before it, made the Minister's prior permission a condition of losing Greek nationality on taking a foreign one. Emigrants almost never asked for it, so they stayed Greek.
What is needed is recognition on paper: a determination of Greek citizenship, filed at the Greek consulate or a Regional Directorate of Nationality in Greece. It leads to entry in the municipal register, from which the identity card and passport follow.
The person's children were born to a Greek parent and are Greek from birth too, except that before 8 May 1984 only a father passed it on. The descent quiz works that through.