Wa alaykum salam wa rahmatuLlahi wa barakatuHu,
Reciting Surah al-Fatihah is obligatory in every rak’ah of every prayer. This includes one leading another in prayer, one following another in prayer, and one praying alone. So yes, one following an imam must recite Surah al-Fatihah.
There are differing opinions related from Imam Shafi’i on this issue. In his commentary on Mukhtasar al-Muzani, the shaykh of the ‘Iraqi tariqah, Shaykh Abu Hamid, related that Imam Shafi’i also has an opinion that in audible prayers one does not recite it. He attributed this opinion to Imam Shafi’s ‘Iraqi School and related it from his Imla’ as well. However, this is not the position on which fatwa is given in the Madhhab.
Fatwa is given on the tarjih of Shaykhan and that of Shaykh al-Islam and his students (like what is stated in Tuhfat al-Muhtaj 2/34). They clearly prefer the view that even in audible prayers one must recite it. In fact, in Rawdah 1/241, Imam Nawawi clearly says the opinion of Imam Shafi’i that one does not recite in audible prayers is weak (ar: qawl da’if). Thus, the opinion of Imam Shafi’i that prescribes it in all prayers for all the aforementioned individuals is mufta bihi.
(Note: a latecomer who joins the prayer while the imam is in ruku’ does not need to recite it. See: Rawdat al-Talibin 1/242)
And Allah knows best.
Answered by Shaykh Yaqub Abdurrahman