Is it permissible for the Imam to lead the obligatory prayer before performing the Sunnah prayer of Fajr if he is late, and is there any sin incurred by his action?

There is no disagreement among scholars regarding the permissibility of performing the obligatory prayer without its preceding voluntary (ratibah) prayer, even if it is the Fajr prayer. However, if the person is an Imam, it is preferable for him to begin with the Sunnah of Fajr and then the obligatory prayer. Nevertheless, if his delay would cause grumbling among the congregants, then it is permissible for him to pray the obligatory prayer first and then make up the preceding Sunnah prayer.