Is it permissible for my husband and his companions to abandon congregational prayer in the public mosque and establish it in one of their homes, under the pretext that they are Salafis and are not allowed to practice the Sunnah of sitting after the Fajr prayer until sunrise in the mosque?

Your husband and his companions should not abandon prayer in the mosque, for it holds immense reward and abundant blessings due to the large congregation. It is more befitting for them to interact with others to teach them the rulings and etiquette of Islam. If they are unable to sit in the prayer area after the Fajr prayer until sunrise, then let them strive in remembering Allah during that time. As for their praying in congregation at home, it is sufficient, and there is no sin upon them for it, even if they miss the virtues of praying in the mosque.