Answered by Ustadha Shazia Ahmad
Does one have to pray his/her Dhuhr prayers after one prays Salat al-Jummah at the masjid?
One who has prayed the Friday prayer is not obliged to pray the dhuhr prayer. If one misses the Friday prayer, it becomes obligatory for him or her to pray the dhuhr prayer.
The only reason one would pray the dhuhr prayer after having prayed the Friday prayer is that if the integrals of the Friday prayer were not fulfilled, thereby invalidating it.
And Allah knows best.
Shazia