Praise be to Allah.
If she wants to earn the reward mentioned in the hadeeth of the Prophet (peace and blessings of Allaah be upon him), “Whoever fasts Ramadaan then follows it with six days of Shawwaal, it will be as if he fasted for a lifetime”
(reported by Muslim, no. 1984), then she should complete her Ramadaan fasts first, then follow it with six days of Shawwaal, so that the hadeeth 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 Ramadaan fasts, provided that she makes them up before the next Ramadaan comes along.