What is the ruling on a husband having sexual intercourse with his wife after the Fajr adhan and 20 minutes before it, and is the fast valid in this case?

If the reliable muezzins consider the mentioned adhan to be for Fajr as-Sadiq (the true dawn), then continuing intercourse after hearing this adhan renders the fast of that day invalid. Since this fast was voluntary and not obligatory, its invalidity incurs nothing other than that it is not religiously recognized, because fasting is abstaining from things that break the fast from Fajr as-Sadiq until sunset.