الجواب وبالله التوفيق
In order for a talaq to take effect, the presence of witnesses is not required, in fact the wife’s own (in person) presence or listening to the issuance of talaq is not required either. Therefore, when you issued the talaq, it took effect immediately. There is no effect on the validity of this talaq based on your father in law’s listening (or not listening) to it.
ذھب جمہور الفقھاء من السلف و الخلف ان الطلاق یقع بدون الشھادۃ (کتاب النوازل، ص۵۳۱، ج ۹
You have mentioned in your question that this “final talaaq” was your first talaq that you have issued, therefore, it will be considered one Talaq-e-Raj‘ai(revocable divorce). There is no need to issue an additional talaq as in the case of Talaq-e-Raj‘ai the husband has a right to perform ruju‘ i.e. to take his wife back during her period of ‘iddah or perform a new Nikah to be together again after her period of ‘iddah.
If for some reason performing new Nikah does not seem suitable then the woman is free to perform Nikah with someone else.
واللہ اعلم بالصواب