Reference: Fataawa al-Lajnah ad-Daa.imah lil-Buhooth al-‘Ilmiyyah wal-Iftaa. – Fatwa No.3475
Fataawa Ramadhaan – Volume 2, Page 693, Fatwa No.698
Question: Is the fasting of the six days [of Shawwaal] a must after the month of Ramadhaan immediately after the day of ‘Eed, or is it permissible [to do so] after ‘Eed by [a number of] days in the month of Shawwaal or not?
Response: It is not a must for him to fast immediately after ‘Eed al-Fitr, rather it is permissible to begin fasting after ‘Eed by a day or [a number of] days. And [also] to fast them continuously or intermittently in the month of Shawwaal according to that which is easy for him. And the issue is quite open in this matter, and it is not obligatory, rather it is a Sunnah.
And with Allaah lies all the success, and may Allaah send prayers and salutations upon our Prophet Muhammad ﷺ and his family and his companions.