Praise be to Allah.
I asked our Shaykh, ‘Abd al-‘Azهz ibn ‘Abd-Allah ibn Baz about this matter, and he replied that hopefully he will be rewarded for that, because it is true that he fasted the six days of Shawwal , and it is also true that he fasted the al-Ayyam al-Beed , and the Bounty of Allah is great indeed.
With regard to this particular matter, Shaykh Muhammad ibn Salih al-‘Uthaymin replied as follows:
“Yes, if he fasts six days of Shawwal , he does not have to fast al-Ayyam al-Beed during that month too, whether he fasted the six days at the same time as al-Ayyam al-Beed (the 13 th, 14th and 15th of the hijri month) or before them or after them, because it is true that he has fasted three days of the month. ‘Aishah (may Allah be pleased with her) said: ‘The Prophet (peace and blessings of Allah be upon him) used to fast three days of every month, and he did not bother whether he fasted them at the beginning of the month or in the middle or at the end.”
This case is similar to that of Tahiyyat al-Masjid (prayer to “greet the mosque” upon entering), which does not have to be done if one prays a regular prayer upon entering the mosque. So if you enter the mosque and pray a regular Sunnah prayer, you do not have to pray Tahiyyat al-masjid…
And Allah knows best.