Is it permissible to propose marriage to a girl who has already been engaged according to Sharia, knowing that there was a previous relationship and a mutual desire to reconcile?

If a marriage contract has been validly concluded for a girl according to Sharia, she is considered the man's wife. It is not permissible to propose to her, based on the Almighty's saying: "And the chaste women from among the believers," regardless of whether consummation has occurred or not. However, if it was merely an engagement and she accepted him, it is also not permissible to propose to her, due to the prohibition of proposing over an existing engagement.