the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
The fasting for the six days of Shawwâl can occur any time during the month of Shawwâl. They may be observed consecutively or separately.
Each fast must have a separate intention.
Scholars differ as to whether the missed days of Ramadân must be made up before observing the six days of Shawwâl.
Some argue that it is obligatory to make up the missed days first.
Their argument is as follows:
Allah's Messenger (peace be upon him) said: "Whoever fasts the month of Ramadan then follows it with six days in the month of Shawwâl, it will be as if he had fasted continuously throughout the year." [Sahîh Muslim (1163)]
They argue that, since the Prophet (peace be upon him): “Whoever fasts the month of Ramadan then follows it with six days in the month of Shawwâl…” therefore the days of Ramadân must be made up in order to follow the Ramadân fasts with the six days of Shawwâl.
Other scholars do not agree with this deduction. They rule that the six days can be observed before making up the missed days of Ramadân. This opinion is easier for those who have missed a lot of days. It is especially easier for women who quite often have a lot of days to make up.
And Allah knows best.
Source: Islam Today