Can the 6 fasts after Ramadan be kept anytime throughout the year or are they limited to Shawwal only?
بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the name of Allah, the Most Gracious, the Most Merciful
There are many virtues regarding the fasting of Shawaal. The Prophet (peace be upon him) mentions fasting in the month of Shawaal is though as one fasted for the whole year. It is permissible that the fasts are not kept continuously and straight after Eid. Meaning the fasts can be kept over a period of 30 days in Shawaal, neither is it important to keep them straight after Eid, what is important they are kept in Shawaal, not any other month.
Only Allah knows best
Written by Maulana Irfan Ali
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 (Fatawaa Rahimiyyah, page 204, Darul Ishat vol 5 to 6)