All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Some jurists mentioned that whoever fasts the six days of Shawwaal with the intention of making up (a missed obligatory fast), vow or the like – such as expiating an oath – he attains the reward of the six days of Shawwaal but not completely. Al-Khateeb Ash-Shirbeeni said: “If one fasts in Shawwaal to make up (a missed obligatory fast), vow or the like, does he attain the reward of the Sunnah or not? I do not know that this matter was mentioned but, apparently, he attains it. However, he does not attain the said reward, especially he who missed Ramadan and made it up in Shawwaal because the aforementioned meaning does not apply to him, (The Prophet's Hadeeth: "Whoever fasts in Ramadan and follows it with six days of Shawwaal, then it is as if he fasted perpetually.") This is why some scholars said that it is recommended for him in this case ( if he could not fast the six days during Shawwaal ) to fast six days in Thul-Qa‘idah because it is recommended to make up for Sunnah fasting. This applies if one adopts the view that the reward is not attained but, if we said that it is attained – as it appears as previously mentioned – then it is not recommended to make anything up for them.
Whoever fasts for the sake of expiating an oath in Shawwaal, this avails him of the obligatory fasting. According to what was stated by Al-Khateeb Ash-Shirbeeni he also attains the original reward of the Sunnah of fasting six days of Shawwaal without attaining the entire reward. Therefore, what is better and more preferable is to single out each of them with separate fasts to attain the promised reward for sure.
Allaah Knows best.