Answer

In the Name of Allah, Most Gracious, Most Merciful. 

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

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In this fatwa:

It is permissible for a woman to delay making up her Ramadan fasts due to menses provided that she makes them up before the next Ramadan and she can observe fasting in Shawwal first.

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Responding to the question, Sheikh M. S. Al-Munajjid, a prominent Saudi Muslim lecturer and author, states: 

If a woman wants to earn the reward mentioned in the hadith of the Prophet (peace be upon him), “Whoever fasts Ramadan then follows it with six days of Shawwal, it will be as if he fasted for a lifetime” (Muslim), she should complete her Ramadan fasts first, then follow it with six days of Shawwal.

With regard to the matter of permissibility, it is permissible for a woman to delay making up her Ramadan fasts due to menses provided that she makes them up before the next Ramadan.

Almighty Allah knows best.

Source: www.islamqa.info