Is marriage to a girl who broke off her engagement and marriage contract to another person—claiming that he was not religious, was an alcoholic, and did not pray—considered Islamically valid, and am I sinful for encouraging her to annul the contract?

Relationships between men and women outside the legal framework are impermissible. If it is merely an engagement and the marriage contract has not been formalized for this young man who does not pray and drinks alcohol, then there is no harm in breaking off the engagement and proposing to her. However, if the marriage contract has been formalized, the girl must refer the matter to the court for annulment or divorce. If your incitement for her to separate from him is due to his bad character, then there is no harm. But if it is merely because you desire to marry her, then it is impermissible and a major sin, as the Prophet (peace be upon him) said: "He is not of us who incites a woman against her husband." Some scholars have even gone so far as to say that the marriage of one who incites a woman against her husband is invalid.