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, may Allaah The Almighty reward you for being keen on consuming what is lawful and avoiding committing what is forbidden.
As regards what you mentioned, then the answer starts from where you stopped. The preponderant opinion in our view,
which corresponds to the justice and rules of inference, is that the person who inherits ill-gotten money is not permitted to take it and he is not permitted to benefit from it even if he is not the one who earned it directly in a forbidden manner. Rather, he is obliged to get rid of it by spending it on the general welfare of the Muslims and give it to the poor and destitute. Even if its amount is not known, one has to endeavor and estimate the amount.
As regards the saving certificates that your deceased father had bought, then what is forbidden from it, which is the Regular Income Certificates (RIC), you should get rid of its interest and benefit from its capital money only.
As regards the Behbood Saving Certificates (BSC), that have a variant income; some scholars issued a Fatwa that it is permissible to invest in it. Thus, it is permissible to benefit from its capital money as well as from its profit. Nonetheless, we cannot give a detailed ruling about it because you did not clarify to us its terms and conditions and the nature of the contract between the investor and the field of investment.
Indeed, we have clarified the conditions of a lawful investment in Fatwa 86125.
As regards what we mentioned concerning the permissibility of benefitting from its profit without issuing a ruling on it, this is because it is mentioned in the question that some scholars issued a Fatwa that it is permissible to invest in it while no mention was made in the question which proves that it is forbidden.
Allaah Knows best.