and they believe that Friday prayer is not held in their locality, while each of the two congregations believes its own Friday prayer to be obligatory.
The questioner may also mean the dawn prayer and the Friday prayer: the dawn prayer is obligatory at its appointed time, and the Friday prayer is obligatory at its appointed time. Between them comes a sermon—the Friday sermon.
Other examples include the sermons delivered during Hajj. The sermon at Arafah comes between the prayer at Arafah and the sunset prayer, both of which are obligatory. The sermon on the Day of Sacrifice comes between the dawn and noon prayers, both of which are obligatory.
He was asked:
Is there a hadith concerning the recitation of Sūrat al-Kahf after the afternoon prayer on Friday?
He replied:
Praise be to Allah. There are reports concerning the recitation of Sūrat al-Kahf on Friday, mentioned by scholars of hadith and jurisprudence. However, these refer generally to Friday without specifying a particular time. I have not heard that this is specifically prescribed after the afternoon prayer. And Allah knows best.