Is the mentioned supplication answered, and will Allah forgive whoever recites it for forty Friday nights for what is between him and other human beings, and him and his Lord?

The aforementioned hadith is fabricated (mawdu'), narrated by Ibn Asakir and Ibn al-Jawzi in "Al-Mawdu'at" with a weak text. Al-Suyuti included it in "Al-La'ali' al-Masnu'ah fi al-Ahadith al-Mawdu'ah," and Al-Albani judged it to be fabricated in "Al-Silsilah al-Da'ifah."