Should the marriage contract for this man be solemnized, or should efforts be made to divorce him, knowing that he married the sister عرفيًا (according to common practice without official documentation) and threatened to expose her matter?

A woman is married off by her legal guardian, who is, in order: the father, then the paternal grandfather, then the son, then the full brother, then the half-brother (from the father's side), then their sons, then the paternal uncles. If a woman marries without her guardian, her marriage is invalid according to the majority of scholars. However, if a Shar'i court ratifies it, the contract becomes valid, and the judge's ruling resolves the dispute. Therefore, the matter rests with your sister: if she wishes, the court can grant her a divorce to alleviate harm, and if she wishes, she can endure it. There is no need to renew the contract, because a marriage over which there is a dispute becomes valid by a judge's ruling. You do not have the right to intervene except with advice and guidance, as long as the court has ratified the marriage.