The Messenger of Allāh صَلَّى اللّٰهُ عَلَيْهِ وَسَلَّمَ said:

“Whoever fasts the [blessed] month of Ramadān and then follows it by fasting six days during the month of Shawwāl will be rewarded as if he had fasted the entire year.”

Saheeh Muslim 1164 | Saheeh

Translation: Authentic Quotes

TN: The fasting person who has to make up fasts from [the blessed month of] Ramadān should not fast the six days from Shawwāl except after making up the fasts of [the blessed month of] Ramadān. These days can be anytime during the month of Shawwāl except the first day [the Day of ‘Eed] because it is unlawful to fast the day of ‘Eed. Shaykh al-Albāni [may Allāh have mercy on him] was asked the best way to fast the six fast of Shawwāl, consecutively or seperately, he replied consecutively, and Allāh knows best.