Answered by Sidi Mostafa Azzam
If your only two choices are going to Friday prayers that start before duhr at a mosque, or prayers that start after duhr in a musalla (not a mosque) on campus/medical center, which is better?
Regarding choice 1: in the Shafi’i school, a condition for a valid Friday (Jumu’ah) Prayer is that the khutbahs and the prayer be within the time of Zuhr (Reliance of the Traveller, f18.7(b) and f18.10(c)). Without the fulfillment of this condition, it is not Jumu’ah, so that is not in fact a choice. That leaves choice 2: in the Shafi’i school, there is no harm in praying the Friday Prayer somewhere other than a mosque, since its being prayed in a mosque is not a condition. The upshot is that it is better to pray it at the musalla after Zuhr (if what you mean by “after duhr” is after Zuhr time has entered, but before it has exited), rather than pray it at the mosque before Zuhr, since before Zuhr it cannot be prayed. Note that this is all with the assumption that all the other conditions of the Friday Prayer are met (see Reliance, f18.7-10).
Is there a distinction between when the khutba starts versus when the prayer starts, i.e. if the khutba starts pre-duhr, but the prayer doesn’t occur unless it is after duhr.
A condition for a valid Friday (Jumu’ah) Prayer is that the khutbahs and the prayer be within the time of Zuhr (Reliance of the Traveller, f18.7(b) and f18.10(c)).