Is it permissible to use the proceeds of usurious money to finish an orphans’ apartment and rent it out for them to live off its income?

It is permissible to give the interest to your deceased nephew's son and daughter if they are poor and do not possess enough to cover their basic needs. They are among the legitimate recipients for spending ill-gotten money, and giving it to them might even be preferable. These funds should be spent on what is most beneficial for them, such as completing and furnishing the apartment.