Fiqh-us-Sunnah Volume 3, Zakaat and Fasting, Fiqh 3.124B.

Abu Ayyub al-Ansari reported that the Prophet, upon whom be peace, said: “Whoever fasts during the month of Ramadan and then follows it with six days of Shawwal will be [rewarded] as if he had fasted the entire year.” This is related by “the group,” except for al-Bukhari and anNasa’i.

According to Ahmad, one may fast on these days consecutively or non-consecutively, as neither practice is preferred over the other. Hanafiyyah and Shaf’iyyah maintain that it is preferable to fast on consecutive days after the ‘id.