What is required of the worshippers who differed in their intention and prayers after the Friday preacher led the Rain Prayer (Salat al-Istisqa) before the Friday Prayer (Salat al-Jumu'ah) without establishing the latter?

The preacher committed violations: he introduced a prayer between the Friday sermon and the [Friday] prayer that was not transmitted from the Prophet, peace and blessings be upon him; he abandoned the immediate succession (muwalat) between the sermon and the prayer; and he caused chaos. The prayer of the imam and those who prayed Jumu'ah with him is valid according to those who do not consider immediate succession obligatory. The majority, however, are of the opinion that it is obligatory to repeat it as Dhuhr prayer, and this is the more preponderant view. Whoever prayed with the intention of Salat al-Istisqa (prayer for rain) must perform the Dhuhr prayer. As for whoever prayed Jumu'ah with the intention of Salat al-Istisqa, the correct view is that it is permissible, but it is more cautious to repeat it as Dhuhr prayer to avoid disagreement.