Is it valid to fast for a continuous month as a vow after a quarrel with a sister, and what is the ruling on this vow and what must be done?

If the intention behind a vow is to encourage or prevent something, it is called a "vow of obstinacy" (nadhr al-lajaj). Scholars have differed regarding its ruling, with several opinions:

1. He must offer an expiation for breaking an oath (kaffarat yamin). 2. He must fulfill what he vowed. 3. He has the choice between offering an expiation for breaking an oath and fulfilling what he vowed, and this is the most preponderant opinion.

The vow of the questioner's brother is a vow of obstinacy and an act of obedience conditional upon committing a sin. Therefore, two things apply to him: breaking the vow by maintaining kinship ties, and then either offering an expiation for breaking an oath or fulfilling the vow, which is to fast for a month.