What is the Islamic ruling on establishing two separate congregational prayers in one mosque, with a wall separating them, knowing that one of them was established prior?

There is no harm in performing a second congregational prayer in a mosque where a prayer has already been performed. This is indicated by the hadith of the man who prayed with the Messenger of Allah, Allah's blessings and peace be upon him, after the people had already prayed, and his (peace be upon him) saying: "These two are a congregation." This is further supported by the actions of Anas ibn Malik (may Allah be pleased with him) and Al-Hasan Al-Basri.

It is preferable for those who arrive late to make the call to prayer (adhan) and the iqama, but there is no harm in relying on theadhan of the people of the mosque.

The permissibility of two congregations praying in the same mosque is conditioned upon the second congregation's delay from the first prayer being due to a legitimate Shar'i excuse, in order to prevent undermining the wisdom of congregational prayer and justifying laziness.

As for praying two congregations in two different mosques, there is no harm in it due to the large number of worshippers, or the distance between mosques, or for any other benefit.