When and how did the Prophet's uncle Abbas ibn Abd al-Muttalib embrace Islam?

In a Nutshell: If my analysis is correct, Al-Abbas (ra) would have embraced Islam as early as the first year after revelation, when he reflected on the message that the Messenger (saw) announced at mount Safa in light of Biblical prophecies he was told about in relation to his nephew. But he publicly announced his Islam with the conquest of Mecca (8th year after Hijrah = 21st year after revelation). Background It is unclear when al-Abbas ibn Abd al-Muttalib (ra) accepted Islam because he only proclaimed Islam publicly very late, after the conquest of Mecca (8th year after Hijrah). He later revealed that he had accepted Islam secretly much earlier. But how and when he accepted Islam is still ambiguous. Abu Rafi, the servant of the Messenger (saw), said: كنت غلامًا للعباس بن عبد المطلب، وكان الإسلام قد دخلنا أهل البيت، فأسلم العباس، وأسلمت أمُّ الفضل، وأَسْلَمْتُ، وكان العباس يكتم إسلامه I was a slave of al-Abbas ibn Abd al-Mutalib. Islam had entered our homes (the homes of the family of the Prophet); Al-Abbas, Umm al-Fadl and I embraced Islam, and al-Abbas kept it secretly.” (Ibn Saad, al-Tabaqat, Vol 4, p. 73) All the scholars and writers of seerah argue that al-Abbas embraced Islam early (saying nothing about how early it was) before he publicly announced it. For example, Ibn Abd al-Bar said: أسلم العباس بن عبدالمطلب رضي الله عنه قبل فتح خيبر، وكان يكتُم إسلامه، ثم أظهر إسلامه يوم فتح مكة Al-Abbas ibn Abd al-Muttalib (ra) before the conquer of Khaybar [7th year after Hijrah], and he was keeping his Islam secret. He then announced his Islam on the day of Mecca conquer.” (Ibn Abd al-Bar, al-Isti'aab, Vol. 3, p. 96) I have tried to search for narrations that could give us hints of the time of his conversion. Here is what I found. Al-Abbas (ra) converted at the dawn of revelation The first time al-Abbas (ra) knew of the message of Islam was at the banquet that the Messenger organized for the leaders of his clan, al-Abbas being one of them. The next time he was seen to be connected closely to the message of Islam is also in the first year after revelation when the Messenger went to mount Safa calling his people publicly. Note: In another answer, I discussed the event of Safa mountain and concluded: This verse was revealed early in the seera, contrary to the traditional view, in the first year of revelation. Around the time this verse was revealed, the Messenger (saw) went to mount Safa. After or before such an event, the Prophet invited his clan to a banquet three times. I recently came across a rare narration in an Arabic historical book published by The Council of Senior Scholars of Al-Azhar, authored by Prof, Muhammad al-Bayumi (d. 2011) titled: Mina al-Qasas al-Islami (من القصص الإسلامي). The narration talks about a later event that occurred at the caliphate of Umar (ra). At the time of drought, Umar (ra) asked al-Abbas (ra) to lead the prayer of al-Istisqa (supplication to Allah for rain). Some Muslims got angry, arguing Ali (ra) should lead the prayer as he accepted Islam very early, well before al-Abbas (ra). Al-Abbas (ra) replied telling them that his conversion was so early, but he publicly announced it later: لقد تأخر إسلامي المعلن إلى قبيل الفتح، ولكنني كنت مسلمًا منذ جهر ابن أخي صلى الله عليه وسلم بالدعوة. وقد أسررت إسلامي لأحاول أن أمنع من أذى قريش للمسلمين ما أستطيع، على أني كنت متيقنًا أنه رسول الله حقًا منذ أعلن خطبته الأولى على الملأ من قريش. My professed Islam was delayed until just before the conquest (of Mecca), but I have been a Muslim since my nephew (saw) openly preached. I kept my Islam secret to try to prevent Quraish from harming Muslims as much as I could, although I was certain that he was truly the Messenger of God since he publicly announced his first sermon in front of Quraysh [most probably referring to the event of Safa mount]. (Muhammad al-Bayumi, Mina al-Qasas al-Islami, al-Azhar print, Vol. 1, p. 11) Al-Abbas (ra) then said that reason he believed in the Messenger is that his call was confirmed by three prophecies of 3 religious rabbis (such as Buhayra) who informed that one of his clan would be a true Messenger of God and they gave the signs of Prophet Muhammad (saw). I can not find this narration in any printed, early historical books that I have access to, so I attribute it to the legitimate entity that published it. If my analysis of the time of Safa mount is true, al-Abbas (ra) would have embraced Islam as early as the first year after revelation, when he reflected on the message that the Messenger (saw) announced at mount Safa in light of the Biblical prophecies he was told about his nephew. Conclusion | When and how al-Abbas converted? If my analysis is true, al-Abbas (ra) would have embraced Islam as early as the first year after revelation, when he reflected on the message that the Messenger (saw) announced at mount Safa in light of Biblical prophecies he was told about in relation to his nephew. References Muhammad al-Bayoumi, Mina al-Qasas al-Islami, al-Azhar print, Vol. 1. Ibn Abd al-Bar, al-Isti'aab, Vol. 3. Ibn Saad, al-Tabaqat, Vol 4.