Is it permissible for a girl to falsely swear an oath denying her previous relationship with a man in order to preserve her honor, provided she repents to Allah, and what should she do in light of her husband's threats and false accusations against her, and his refusal to divorce her?

The wife erred by informing her fiancé of her transgression, as this unveiled what Allah had concealed, leading to ill-will and the husband's extortion of her money. There is no blame on her if she denies committing the transgression and swears an oath to that effect, in order to avert harm. It is preferable to use allusive and ambiguous language (ta'rid and tawriya) instead of outright lying. What the husband did by taking her money through threats is an injustice and invalid. If he forced her into a khul’ (divorce at the wife’s instance), her khul’ is invalid, and she retains her rights.