All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
The Shafie'e jurists stated that it is permissible to combine the afternoon prayer with Friday prayer due to rain save if the conditions of combining prayers are met as mentioned earlier in Fatwa No. (501). Moreover, the evidence on this that Friday prayer is a replacement of the noon prayer so they take the same ruling and it is permissible to combine Friday prayer with the noon prayer as is the case when combining the afternoon prayer with noon prayer because the timing of Friday prayer is the same as the timing of noon prayer.
In conclusion, Al-Khateeb Al-Sharbini (May Allah have mercy on his soul) said (What means):" Combining the afternoon prayer with Friday prayer is permissible in case it was raining at the very moment of performing the prayer." [Mughni Al-Muhtaj 1/534]. And Allah knows best.