The Muslim Moses agreed with Christians about original sin in Islam

82 Divine Will (Al-Qadar)
(11)Chapter: Adam and Musa argued with each other in front of Allah(11)باب تَحَاجَّ آدَمُ وَمُوسَى عِنْدَ اللَّهِ
Narrated Abu Huraira:
The Prophet (ﷺ) said, “Adam and Moses argued with each other. Moses said to Adam. ‘O Adam! You are our father who disappointed us and turned us out of Paradise.’ Then Adam said to him, ‘O Moses! Allah favored you with His talk (talked to you directly) and He wrote (the Torah) for you with His Own Hand. Do you blame me for action which Allah had written in my fate forty years before my creation?’ So Adam confuted Moses, Adam confuted Moses,” the Prophet (ﷺ) added, repeating the Statement three times.
حَدَّثَنَا عَلِيُّ بْنُ عَبْدِ اللَّهِ، حَدَّثَنَا سُفْيَانُ، قَالَ حَفِظْنَاهُ مِنْ عَمْرٍو عَنْ طَاوُسٍ، سَمِعْتُ أَبَا هُرَيْرَةَ، عَنِ النَّبِيِّ صلى الله عليه وسلم قَالَ ‏ “‏ احْتَجَّ آدَمُ وَمُوسَى، فَقَالَ لَهُ مُوسَى يَا آدَمُ أَنْتَ أَبُونَا خَيَّبْتَنَا وَأَخْرَجْتَنَا مِنَ الْجَنَّةِ‏.‏ قَالَ لَهُ آدَمُ يَا مُوسَى اصْطَفَاكَ اللَّهُ بِكَلاَمِهِ، وَخَطَّ لَكَ بِيَدِهِ، أَتَلُومُنِي عَلَى أَمْرٍ قَدَّرَ اللَّهُ عَلَىَّ قَبْلَ أَنْ يَخْلُقَنِي بِأَرْبَعِينَ سَنَةً‏.‏ فَحَجَّ آدَمُ مُوسَى، فَحَجَّ آدَمُ مُوسَى ‏”‏ ثَلاَثًا‏.‏ قَالَ سُفْيَانُ حَدَّثَنَا أَبُو الزِّنَادِ، عَنِ الأَعْرَجِ، عَنْ أَبِي هُرَيْرَةَ، عَنِ النَّبِيِّ صلى الله عليه وسلم مِثْلَهُ‏.‏
Reference : Sahih al-Bukhari 6614
In-book reference : Book 82, Hadith 20
USC-MSA web (English) reference : Vol. 8, Book 77, Hadith 611
http://sunnah.com/bukhari/82/20

Qur’an 2:

30 And (remember) when your Lord said to the angels: “Verily, I am going to place (mankind) generations after generations on earth.” They said: “Will You place therein those who will make mischief therein and shed blood, – while we glorify You with praises and thanks and sanctify You.” He (Allah) said: “I know that which you do not know.”

31 And He taught Adam all the names (of everything) , then He showed them to the angels and said, “Tell Me the names of these if you are truthful.”

32 They (angels) said: “Glory be to You, we have no knowledge except what you have taught us. Verily, it is You, the All-Knower, the All-Wise.”

33 He said: “O Adam! Inform them of their names,” and when he had informed them of their names, He said: “Did I not tell you that I know the Ghaib (Unseen) in the heavens and the earth, and I know what you reveal and what you have been concealing?”

34 And (remember) when We said to the angels: “Prostrate yourselves before Adam.”. And they prostrated except Iblis (Satan), he refused and was proud and was one of the disbelievers (disobedient to Allah).

35 And We said: “O Adam! Dwell you and your wife in the Paradise and eat both of you freely with pleasure and delight, of things therein as wherever you will, but come not near this tree or you both will be of the Zalimun (wrong-doers).”

36 Then the Shaitan (Satan) made them slip therefrom (the Paradise), and got them out from that in which they were. We said: “Get you down, all, with enmity between yourselves. On earth will be a dwelling place for you and an enjoyment for a time.”

37 Then Adam received from his Lord Words. And his Lord pardoned him (accepted his repentance). Verily, He is the One Who forgives (accepts repentance), the Most Merciful.

38 We said: “Get down all of you from this place (the Paradise), then whenever there comes to you Guidance from Me, and whoever follows My Guidance, there shall be no fear on them, nor shall they grieve.

39 But those who disbelieve and belie Our Ayat (proofs, evidence, verses, lessons, signs, revelations, etc.) – such are the dwellers of the Fire. They shall abide therein forever.

40 O Children of Israel! Remember My Favour which I bestowed upon you, and fulfil (your obligations to) My Covenant (with you) so that I fulfil (My Obligations to) your covenant (with Me), and fear none but Me.

41 And believe in what I have sent down (this Qur’an), confirming that which is with you, [the Taurat (Torah) and the Injeel (Gospel)], and be not the first to disbelieve therein, and buy [get (تاخذ اجرا)] not with My Verses [the Taurat (Torah) and the Injeel (Gospel)] a small price (i.e. getting a small gain by selling My Verses), and fear Me and Me Alone. (Tafsir At-Tabari ).

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