The Ruling on Changing the Place of Prayer for the Sunnah
Has any proof been reported for changing one’s place in order to perform the Sunnah following the obligatory prayer?
Yes, it has been reported in the Hadith of Mu’awiyah that he said: The Prophet (sallallaahu alaihi wa sallam) 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.
 Muslim no. 883 and Abu Dawud no. 1129
Shaykh Muhammad bin Saalih al-`Uthaymeen
Fatawa Islamiyah Vol.2 Page 314
This is from Fatawa Islamiyah Vol. 2 page 314