The Ruling on Changing the Place of Prayer for the Sunnah
Question :
Has any proof been reported for changing one's place in order to perform the Sunnah following the obligatory prayer?
Answer:
Yes, it has been reported in the Hadith of Mu'awiyah that he said: "The Prophet ordered us not to join one prayer with another prayer without leaving or speaking (in between),"
So the scholars have understood from this that a gap must be made between the obligatory and the Sunnah either by speaking or by changing one's place.
Source:
Ibn 'Uthaimin
Fatawa Islamiyah, Vol. 2 Pages 314-315