Is it permissible to close the doors of the mosque and separate the inner sanctuary from the worshipers outside for Friday prayer, given that there are incomplete rows inside the mosque?

The reason for closing the mosque before the rows are complete is unknown. The default ruling is that this is not permissible because it prevents worshippers from entering the mosque without right, and it contradicts the Sunnah (definition) regarding completing the rows. The prayer of those outside is valid if they hear or see the Imam, or hear or see someone praying with him.