I made a vow to Allah, the Exalted, to fast a whole month, but I want to feed poor people instead. Please note that I am able to fast. Is it permissible for me to do so?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.

Allaah, the Exalted, commanded us to fulfill our vows. He said (what means): {… and fulfill their vows…} [Quran 22:29]

Allaah, the Exalted, praised His pious slaves from among  the people of Paradise, saying (what means): {They [are those who] fulfill [their] vows and fear a Day whose evil will be widespread.} [Quran 76:7] Therefore, the vow-taker is obliged to fulfill his vow exactly in the very manner that he had vowed. Changing the vow or offering a substitute of the vowed object is not a valid fulfillment of the vow unless he is totally and permanently unable to fulfill it. In such case, the vow-taker should offer an expiation like that for breaking an oath. Therefore, it is impermissible for you to feed poor people or do anything instead of fasting a whole month as you had vowed, as long as you are able to fast and you are not experiencing a case of inability that is not likely to end.

Allaah Knows best.