What is the ruling on a husband abandoning his wife whom he married customarily without her family's knowledge, and how can he be persuaded to complete the legal marriage and repent?

Marriage without a guardian (wali) is invalid according to the majority of scholars. Moreover, neglecting to document the marriage contract can lead to significant harms and the loss of critical legal rights, such as lineage and inheritance. It is obligatory to repent to Allah and for this woman to leave this man, and he must divorce her. Then, if he wishes to marry her, he must conclude a legitimate marriage contract that fulfills all conditions and pillars. Despite this contract being invalid according to the majority, it does have certain recognized effects, such as establishing lineage and inheritance.