Is it permissible for my wife to use pills to postpone her menstrual period to be able to fast the whole month of Ramadan?

It is not permissible for menstruating women to fast or pray. If menstrual flow stops naturally or by taking medicine, there is then no objection to fasting and praying.

The ruling
It is permissible to take pills to delay menstruation provided they are prescribed by a physician to avoid harm, following the legal maxim that states: "Do not cause harm and do not reciprocate harm."
And God the Almighty knows best.