Wa `alaykum As-Salamu waRahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, we would like to thank you for the great confidence you place in us, and we implore Allah Almighty to help us serve His cause and render our work for His Sake.
In his response to the question, Sheikh Muhammad Saleh Al-Munajjid, a prominent Saudi Islamic lecturer and author, stated:
There are no sound hadiths concerning reading Surat Aal `Imraan on Friday. All the reports that have been narrated concerning that are either very weak or fabricated.
It was narrated that Ibn ‘Abbas said: “The Prophet (peace and blessings of Allah be upon him) said: ‘Whoever recites the Surah in which the family of `Imran (Aal ‘Imran) are mentioned on Fridays, Allah and His angels will send blessings upon him until the sun sets.’”
(Narrated by Al-Tabarani in al-Mu`jam al-Awsat, 6/191; and Al-Kabir, 11/48. This hadith is very weak or fabricated).
Al-Haythami said, “the isnad of this hadith includes Talhah ibn Zayd al-Riqqi, who is very weak.” (Majma’ al-Zawa’id, 2/168).
Ibn Hajar said: Talhah is very weak, and Ahmad and Abu Dawud accused him of fabricating reports. (See Fayd al-Qadir, 6/199)
Sheikh Al-Albani said: “this hadith is fabricated”. (See hadith no. 5759 in Da`if al-Jami`)
Al-Taymi narrated in al-Targheeb that “Whoever recites Surat al-Baqarah and Surat Aal `Imran on the night of Jumu`ah will have reward like that which is between the seventh earth and the seventh heaven.”
Al-Mannawi said: “this hadith is strange and very weak).(Fayd al-Qadir, 6/199)
Allah Almighty knows best.