Is it permissible to offer the Sunnah prayer after Dhuhr before the the prescribed remembrances (adhkar) due to work commitments?

If you are preoccupied from performing all the prescribed remembrances (adhkar) before a supererogatory (nafilah) prayer, you should perform some of them, even if only a few, especially if the nafilah prayer is in the place of a fard (obligatory) prayer. This is to avoid the prohibition of connecting one prayer to another until one speaks or leaves. What you are unable to perform may be made up after the supererogatory prayer, following the example of the Prophet, peace and blessings be upon him, and Al-Nawawi's statement on the necessity of making up missed remembrances. However, this should not become a permanent habit, but only when needed.