Answer
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.
In this fatwa:
The narration you mentioned about reciting Surat Hud on Friday is a weak narration.
Answering your question, The Fatwa Center at Islamweb, states:
The narration which reads: “Recite surat Hud on Friday“, is not correct to be attributed to the Prophet (peace be upon him) as it is a mursal hadith.
The narration is reported by Kab Al-Ahbar and he is one of the Followers (the generation that followed that of the Companions) and he did not see or meet the Prophet.
A mursal hadith is a narration on the authority of some of the Followers and it is one of the categories of weak hadiths
Sheikh Al-Albani classified this narration as weak) in his Da`eef Al-Jami`.
When reviewing the Musnad of Ad-Daarimi, Sheikh Husayn Saleem Asad said about this hadith: “Its chain of narrators is weak because it is a mursal hadith.”
Almighty Allah knows best.
Source: www.islamweb.net