Is what the sister did, swearing falsely upon the Mushaf, an oath of immersion (yamin ghamus), and what is its expiation?

If a woman accuses you truthfully and swears falsely to exonerate you, she must repent and seek forgiveness, without expiation, because expiation is required for a binding oath, not for a deliberate false oath. As for you, it was not permissible for you to lie to her; rather, you should have denied the accusation against her and accused her of slander if you were innocent. You must repent, seek forgiveness, and perform righteous deeds.