Answered by Shaykh Faraz Rabbani
If one walks into the university prayer room or mosque and has not prayed the 4 sunnah of dhuhr, should he join the congregation if it is already in progress?
1. Definitely. One should join the congregation, for it is more strongly emphasized than the pre-fard sunna prayer, and then pray the pre-fard sunna after the obligatory prayer, except at Fajr and Asr times. At these two times, it is not permitted to pray any non-obligatory prayers after the obligatory one. [Shurunbulali, Imdad al-Fattah Sharh Nur al-Idah; Ibn Abidin, Radd al-Muhtar]
2. At Fajr time, however, one should pray the pre-fard sunna even if the congregation is in progress, but only if sure that one will catch the congregation before the imam’s final salams. [ibid.]
And Allah alone gives success.