Questions Concerning the Fasts of Shawwāl
Answering queries related to the six-day fasts of Shawwāl and the priority in respect to making up the missed fasts of Ramaḍān.
If someone has missed some of the days of Ramaḍān, he should fast them first, then fast six days of Shawwāl, because he cannot follow the fast of Ramaḍān with six days of Shawwāl unless he has completed his Ramaḍān fast.
DO THE FASTS HAVE TO BE DONE IMMEDIATELY AFTER RAMAḌĀN?
[Q]: ‘Should fasting the six days be done immediately after Ramaḍān, following the day of ’Eed or is it permissible to do it a few days after ’Eed in the month of Shawwāl or not?’
[A]: ‘‘These days do not have to be fasted immediately after ’Eedul-Fitr; it is permissible to start fasting them one or more days after ’Eed, and they may be done consecutively or separately during the month of Shawwāl, according to what is easier for a person. There is plenty of room for maneuver in this matter, and this is not obligatory, it is Sunnah. And Allāh is the Source of strength. May Allāh bless our Prophet Muḥammad and his Family and Companions and grant them peace.’’ 
THE FASTS OF SHAWWĀL OR THE FASTS OF RAMAḌĀN?
[Q]: ‘If a person fasts six days of Shawwāl after Ramaḍān when he has not yet completed the Ramaḍān fast - because he did not fast ten days of Ramaḍān for a legitimate reason - will he have the same reward as a person who fasted all of Ramaḍān and followed it with six days of Shawwāl. Meaning, will he be like a person who fasted for a lifetime? Please explain to us, may Allāh reward you with good?’
[A]:‘‘The precise rewards for the deeds which people do for the sake of Allāh is something which is known only to Allāh. If a person seeks the reward from Allāh and strives to obey Him, his reward will not be lost, as Allāh says,
‘‘We shall not make the reward of anyone who does his (righteous) deeds in the most perfect manner to be lost.’’ [Sūrah-Kahf 18:30]
If someone has missed some of the days of Ramaḍān, he should fast them first, then fast six days of Shawwāl, because he cannot follow the fast of Ramaḍān with six days of Shawwāl unless he has completed his Ramaḍān fast. And Allāh is the source of strength. May Allāh bless our Prophet Muḥammad and his Family and Companions, and grant them peace.’’ 
FASTING THE SIX DAYS OF SHAWWĀL EVERY YEAR:
[Q]: ‘If someone fasts six days of Shawwāl, then one year he gets sick or something prevents him from fasting, or he is too lazy to fast, will there be any sin on him? We have heard that if a person fasts these six days one year, he must never give up this practice thereafter.’
[A]: ‘‘Fasting six days of Shawwāl after the day of ’Eed is Sunnah. It is not wājib (obligatory) on the person who does this once or more often to continue doing it. He is not guilty of a sin if he does not fast these days. And Allāh is the Source of strength. May Allāh bless our Prophet Muḥammad and grant him peace.’’ 
 Fatāwá al-Lajnatud-Daa‘imah (10/391)
 Ibid (10/392)
 Ibid (10/391)