Is it permissible to pray the فرض (obligatory) Dhuhr prayer and then perform the Sunnah later due to time constraints at school?

The original principle is to pray the Sunnah (pre-prayer voluntary prayers) before the obligatory prayer. However, for someone who missed it due to preoccupation or similar reasons, they may perform it after the obligatory prayer, or after the post-prayer regular Sunnah (Ar-Ratibah Al-Ba'diyah); this is based on what was authentically reported from Aisha, that the Prophet, peace and blessings be upon him, if he did not pray four rak'ahs before Dhuhr, he would pray them after it. And if he missed the four (rak'ahs) before Dhuhr, he would pray them after the two rak'ahs after Dhuhr. Therefore, there is no harm in praying the pre-prayer regular Sunnah after the obligatory prayer for someone who is unable to perform it before the prayer.