If a person does not fast six days in Shawwal, can he fast them in Dhu’l-Qa’dah?
Question

A woman fasted four of the six days of Shawwal, then her period came at the end of Shawwal and she did not complete the six days. She only has two days left. Can she complete the six days of Shawwal after Shawwal or not?.
Praise be to Allah.Muslim narrated in his Saheeh (1164) from Abu Ayyoob al-Ansaari (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “Whoever fasts Ramadan then follows it with six days of Shawwal, it is as if he fasted a lifetime.” 
The apparent meaning of the hadeeth is that this reward can be attained only by the one who fasts six days in Shawwal. 
The scholars differed concerning one who fasts the six days at a time other than Shawwal, whether that is due to an excuse or not. Does he attain the virtue of fasting them in Shawwal or not? There are two views. 
(i)
A number of Maalikis, and some Hanbalis are of the view that this virtue may be attained by the one who fasts six days in Shawwal and afterwards, and that the hadeeth only mentioned Shawwal in order to make things easier, because fasting them after Ramadan is easier than doing it later on. 
Al-‘Adawi said in his commentary on Sharh al-Khurashi (2/243): The Lawgiver only mentioned Shawwal in order to make it easier with regard to fasting, not to restrict the ruling to that time only. No doubt doing it in the first ten days of Dhu’l-Hijjah along with what was narrated concerning the virtue of fasting at that time is better, because the purpose is achieved in addition to the extra reward for fasting on virtuous days. Doing it in Dhu’l-Qa’dah is also good. To sum up: The later you fast them, the greater the reward because it is more difficult. End quote. 
It was narrated in Tahdheeb Furooq al-Quraafi by Muhammad ibn ‘Ali ibn Husayn, the mufti of the Maalikis in Makkah, and printed with al-Furooq (2/191), from Ibn al-‘Arabi al-Maaliki, that the words of the Prophet (peace and blessings of Allah be upon him) “in Shawwal” are mentioned by way of example, and that what is meant is that fasting Ramadan counts as ten months, and fasting six days of Shawwal counts as two months, and that is the view of the madhhab of Imam Maalik. If that is at a time other than Shawwal then the ruling is the same. He said: This is very smart so learn it. End quote.  
Ibn Muflih said in al-Furoo’ (3/108): It is possible that the reward may be attained even when fasting them at a time other than Shawwal, according to some scholars. This was mentioned by al-Qurtubi, because the virtue of that is based on the fact that one good deed (hasanah) will be rewarded tenfold, as it says in the report of Thawbaan. And the recommendation of fasting in Shawwal is because it is easier to fast as one is already used to fasting, and this is a kind of dispensation, and it is more appropriate to avail oneself of the dispensation.  
It was also quoted by the author of al-Insaaf, who commented on it by saying: I say: This view is weak and is contrary to the hadeeth. Rather it is connected to the virtue of Ramadan because it comes immediately after it and not because the good deed is rewarded tenfold, and because fasting them is equal to the obligatory fast of Ramadan in virtue. End quote from al-Insaaf (3/344). 
(ii)
A number of the Shaafa’is were of the view that a person who does not fast six days in Shawwal can make it up in Dhu’l-Qa’dah, but the reward will be less than that of the one who fasts them in Shawwal. The person who fasts Ramadan and follows it with six days of Shawwal will have the reward of fasting a whole year of obligatory fasts, unlike the one who fasts Ramadan and six days other than in Shawwal. He will have the reward of Ramadan and the reward of six naafil days. 
Ibn Hajar al-Makki said in Tuhfat al-Muhtaaj (3/456): If a person fasts them along with Ramadan every year, it will be like observing obligatory fasts for a lifetime, without multiplying the reward. If he fasts six other days, it will be like observing naafil fasts, without multiplying the reward. End quote.  
(iii)
He can only attain this virtue by fasting them in Shawwal. This is the view of the Hanbalis. 
It says in Kashshaaf al-Qinaa’ (2/338): The virtue of fasting them – i.e., the six days of Shawwal – cannot be attained at any time other than Shawwal, because of the apparent meaning of the reports. End quote. 
But there is the hope that the person who fasted some of them and could not complete them because of an excuse will attain the reward and virtue thereof. 
Shaykh Ibn Baz (may Allah have mercy on him) said: It is not prescribed to make them up after the end of Shawwal, because they are Sunnah and the time for them has passed, whether one missed them for an excuse or otherwise. 
He said concerning one who fasted four days in Shawwal and did not complete six because of circumstances: Fasting the six days of Shawwal is a mustahabb act of worship but is not obligatory; but you will have the reward of whatever you fast of them, and there is the hope of a complete reward if there was a legitimate shar’i excuse for not completing them, because the Prophet (peace and blessings of Allah be upon him) said: “If a person falls sick or travels, Allah will decree for him (the reward of) what he used to do when he was not travelling and was healthy.” Narrated by al-Bukhaari in his Saheeh. So you do not have to make up what you did not do. And Allah is the Source of strength. End quote from Majmoo’ Fataawa al-Shaykh Ibn Baz (15/389, 395). 
To sum up: 
Fasting six days at a time other than Shawwal: some scholars regarded that as being like fasting them in Shawwal, and some stated that there is virtue therein but it is less than the virtue of fasting six days in Shawwal. And some scholars hope for the reward for the one who is not able to complete six days because of an excuse. The bounty of Allah is great and His generosity knows no end. If this sister fasted two days in Dhu’l-Qa’dah to make up for what she missed of Shawwal, that is good, and there is the hope that she will be rewarded in sha Allah. 
And Allah knows best.