All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, you should know that a Fatwa is not enough in matters of disputes, so in our view, you must consult a legitimate Islamic court, which is more appropriate for investigating such a case as the judge would listen to both parties and request evidence or swearing an oath if necessary.
If there are disputes on some issues, then ruling of the judge is decisive in such disputes in issues of Ijtihaad (personal reasoning by competent scholars in matters untackled by the Quran and Sunnah). In addition to this, his ruling, unlike a Fatwa, is binding on both parties. For more benefit, please refer to Fatwa 89707.
We will mention here the statement of the Hanafi scholars about the matter; for example, ad-Durr al-Mukhtaar reads:
“If he (the husband) claims Khul‘ in return for money while she (the wife) denies it, then divorce takes effect by his testimony, and the claim about the money is judged according to the principle known in lawsuits; so the statement (that is taken into account) is her statement because she denies it.
The commentary about it in the footnote reads: His saying, "Divorce takes effect by his testimony" means irrevocable divorce, although the money (compensation) is not confirmed because the wording of Khul‘ that is testified is indirect, so an irrevocable divorce takes place as mentioned in his saying, "according to the principle known in lawsuits" – meaning as it is known in lawsuits that the statement that is taken into account is that of the one who denies it and the claimant must provide evidence.”
What this statement means is that the divorce takes place, and the compensation taken from the wife is not confirmed without evidence.
The Hanbali School of jurisprudence stated the same.
Allaah Knows best.