Question: I have heard that according to the Hanafi Madhhab, it is better to remain silent between the fardh and the following sunnah prayers and that one should do the sunnah immediately after the fardh and do the dhikr after completion of the salat. Is that correct?
And why is it like that if there are authentic hadeeth tell us to do dhikr after fard prayer?
Answer: You do not remain silent, but pray the sunnah, if any, after saying "Allahumma anta-as-Salaamu wa mink-as-salaam tabaarakta yaa dhal jalaali wa-l-ikraam," because (as is mentioned by Ibn Aabideen) Muslim and Tirmithiy related from Aa'ishah that the Prophet (may Allah raise his rank) did not sit longer than what it takes to say this after prayer. What is related about other dhikr and du^aa' is for after the sunnah - if there is a sunnah.
... and Allah knows best.