Praise be to Allah.
If she wants to earn the reward mentioned in the hadith of the Prophet (peace and blessings of Allah 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, no. 1984), then she should complete her Ramadan fasts first, then follow it with six days of Shawwal , so that the hadith will be applicable to her too, and she will gain the reward mentioned in it.
As regards the matter of permissibility, it is permissible for her to delay making up her Ramadan fasts , provided that she makes them up before the next Ramadan comes along.
And Allah knows best.