Is it the case that the three divorces are counted based on the wife's belief that the husband does not remember the third divorce, or are they considered only two divorces due to his forgetfulness?

If the wife is certain that her husband has divorced her irrevocably (thrice), either by hearing it herself or by the testimony of two just witnesses, then it is impermissible for her to allow him access to her, and she must abstain from him. This is the ruling for the woman concerning the matter between her and Allah. As for a judicial ruling, the husband's word is accepted if he denies the divorce, unless the wife has evidence in the form of the testimony of two just witnesses. If they differ on the number of divorces, his word is also accepted. As for the man, he is not obligated to accept his wife's word if he has forgotten the divorce, unless there is evidence. However, it is more cautious for him to leave her if she is trustworthy and has no personal interest in her claim.