Is it permissible to complete the marriage with the dowry previously written to ensure civil rights, after the consent of both families, given that the girl "married herself" in the contract written by two notaries?

A girl corresponding with a non-mahram man and attempting to elope with him is a grave evil and corruption. They both must repent. If the marriage took place without a formal contract or witnesses, it is void. If it took place with a formal contract and witnesses, it is void according to the majority of scholars but valid according to Abu Hanifa. The contract must be rectified by fulfilling its conditions. The dowry (mahr) is not a condition or pillar of marriage according to the majority of scholars; thus, the contract is valid without it, based on Allah's saying: "There is no blame upon you if you divorce women before consummating the marriage or before specifying for them a mahr."