The reward of fasting the six days of Shawwaal is not attained except if a person has completed the month’s fasts of Ramadhan, so whoever has some missed fasts from Ramadhan then let him not fast the six days of Shawwaal until he has completed the missed fasts of Ramadhan, because the Prophet sallallaahu 'alaihi wasallam said:
من صام رمضان ثم أتبعه بست من شوال
Whoever fasts Ramadhan then follows that with six from Shawwaal… [Muslim, Abu Dawud, Tirmidhi, Ibn Majah, Ahmad, ad-Daarimi].
So based upon this, we say to anyone who has missed fasts, upon him is that he must fast those first, then fast the six days of Shawwaal. And if it happens that these six days fall upon a Monday or Thursday then indeed he will attain the reward of them both [the six days and the fasting upon the Monday or Thursday], with the reward of the intention of fasting the six days and with the reward of the intention for fasting Monday or Thursday, due to his sallallaahu 'alaihi wasallam's saying:
إنماالأعمال بالنتات وإنما لكل امرئ ما نوى
Actions are judged by their intentions and for every person is that what he intended