✅ Answer: Consider the following narration:

مُحَمَّدُ بْنُ الْحَسَنِ بِإِسْنَادِهِ عَنْ سَعْدٍ عَنْ مُحَمَّدِ بْنِ الْوَلِیدِ الْخَرَّازِ عَنْ أَبَانِ بْنِ عُثْمَانَ عَنْ عَبْدِ الرَّحْمَنِ بْنِ أَبِی عَبْدِ اللَّهِ عَنْ أَبِی عَبْدِ اللَّهِ فِی الرَّجُلِ یَدْخُلُ الرَّکْعَةَ الْأَخِیرَةَ مِنَ الْغَدَاةِ مَعَ الْإِمَامِ فَقَنَتَ الْإِمَامُ أَ یَقْنُتُ مَعَهُ قَالَ نَعَمْ وَ یُجْزِیهِ مِنَ الْقُنُوتِ لِنَفْسِهِ

📚 Tahdhib, Vol. 2, p. 316

It was asked from Imam Sadiq (peace be upon him) about someone who joins the congregational Fajr prayer in the second rak'ah while the Imam is performing Qunoot. Should the follower also perform Qunoot with the Imam? The Imam replied: Yes, and this will suffice for their own Qunoot.

✅ Meaning, they do not need to perform Qunoot again in their own second rak'ah. The Qunoot performed with the Imam in the first rak'ah is sufficient.

اللَّهُمَّ فَصَلِّ عَلَی مُحَمَّدٍ وَ آلِ مُحَمَّدٍ وَ عَجِّلْ لِوَلِیِّکَ الْفَرَجَ وَ الْعَافِیَةَ وَ النَّصْرَ