Tafsir Ibn Kathir -> Surah Al-A'raf -> Musa picked up the Tablets when His Anger subsided

Allah said next,

﴿وَلَمَّا سَكَتَ﴾

(And when calmed) and subsided,

﴿عَن مُّوسَى الْغَضَبُ﴾

(the anger of Musa) with his people,

﴿أَخَذَ الاٌّلْوَاحَ﴾

(he took up the Tablets), which he had thrown out of jealousy for Allah and anger for His sake, because of his people worshipping the calf,

﴿وَفِى نُسْخَتِهَا هُدًى وَرَحْمَةٌ لِّلَّذِينَ هُمْ لِرَبِّهِمْ يَرْهَبُونَ﴾

(and in their inscription was guidance and mercy for those who fear their Lord.) Several scholars of Tafsir said that when Musa threw the Tablets on the ground they were shattered and he collected the pieces afterwards. Musa found in its inscription guidance and mercy, but the specific details of the Law was lost, so they said. They also claimed that the shattered pieces of the Tablets still remained in the treasury safes of some Israelite kings until the Islamic State came into existence. Only Allah knows if these statements are true.

﴿وَاخْتَارَ مُوسَى قَوْمَهُ سَبْعِينَ رَجُلاً لِّمِيقَـتِنَا فَلَمَّا أَخَذَتْهُمُ الرَّجْفَةُ قَالَ رَبِّ لَوْ شِئْتَ أَهْلَكْتَهُم مِّن قَبْلُ وَإِيَّـىَ أَتُهْلِكُنَا بِمَا فَعَلَ السُّفَهَآءُ مِنَّآ إِنْ هِىَ إِلاَّ فِتْنَتُكَ تُضِلُّ بِهَا مَن تَشَآءُ وَتَهْدِى مَن تَشَآءُ أَنتَ وَلِيُّنَا فَاغْفِرْ لَنَا وَارْحَمْنَا وَأَنتَ خَيْرُ الْغَـفِرِينَ - وَاكْتُبْ لَنَا فِى هَـذِهِ الدُّنْيَا حَسَنَةً وَفِي الاٌّخِرَةِ إِنَّا هُدْنَـآ إِلَيْكَ قَالَ عَذَابِى أُصِيبُ بِهِ مَنْ أَشَآءُ وَرَحْمَتِى وَسِعَتْ كُلَّ شَىْءٍ فَسَأَكْتُبُهَا لِلَّذِينَ يَتَّقُونَ وَيُؤْتُونَ الزَّكَـوةَ وَالَّذِينَ هُم بِـَايَـتِنَا يُؤْمِنُونَ ﴾

(155. And Musa chose out of his people seventy (of the best) men for Our appointed time and place of meeting, and when they were seized with a violent earthquake, he said: "O my Lord, if it had been Your Will, You could have destroyed them and me before; would You destroy us for the deeds of the foolish among us It is only Your trial by which You lead astray whom You will, and keep guided whom You will. You are our protector, so forgive us and have mercy on us: for You are the best of those who forgive.) (156. "And ordain for us good in this world, and in the Hereafter. Certainly we have Hudna unto You.'' He said: (As to) My punishment I afflict therewith whom I will and My mercy embraces all things. That (mercy) I shall ordain for those who have Taqwa, and give Zakah; and those who believe in Our Ayat.)