What is the ruling on money acquired from proving a fictitious employment relationship to enable the heirs of the deceased to receive a pension from the state, and is repentance for it permissible despite the inability to return the money?

Establishing a non-existent relationship between two parties is considered forgery, falsehood, and unlawful (haram) in Islamic law. The money acquired from it is ill-gotten (suht). One must repent to Allah. The money acquired from this deception and forgery is not to be returned to the one who paid it for their unlawful purpose. You do not own it in exchange for the unlawful benefit. Therefore, its rightful recipients are the poor and the needy, and if you are poor, you may take from it what suffices your need. This also applies to those who have received such salaries unjustly; they must stop their disbursement in a way that does not cause them harm.