If someone missed the Fajr prayer, then prayed Jumu'ah, should he repeat the Dhuhr prayer with four rak'ahs after the Fajr prayer?

Commentators on Khalil's Mukhtasar stated that whoever repeats the Friday prayer (Jumu'ah) after its initial performance should repeat it as Jumu'ah if a mosque where it is performed is available. Otherwise, they should repeat it as Dhuhr (noon prayer) with four rak'ahs. Missed prayers must be made up upon remembrance. Sheikh al-Islam (Ibn Taymiyyah) mentioned that making up a missed prayer during the Friday sermon is obligatory if it is possible to do so and still catch the Jumu'ah prayer, because the prohibition of prayer during the sermon does not include obligatory prayers.