Does the time for the last third of the night end with the first call to prayer or the second, and is it permissible to offer voluntary prayers between them?

The last third of the night ends with the advent of Fajr (the last call to prayer). Voluntary prayers are permissible at this time, and it is considered one of the best times for worship, as Allah (the Most High) descends to the lowest heaven and says: "Who is there that calls upon Me, that I may answer him? Who is there that asks of Me, that I may give him? Who is there that seeks My forgiveness, that I may forgive him?"