Is it permissible to forge documents to claim the purchase of a house before its owner's death, knowing that most of its price came from the deceased father's money, and that the state is the legal heir due to the absence of any other heir, and fearing homelessness should the state seize it?

The house belongs to the grandfather's wife. Since the public treasury (Bayt al-Mal) is not organized, it does not inherit; rather, the money of one who has no heir is spent on the general welfare of Muslims. Scholars have stipulated the permissibility for a Muslim to make a legal stratagem concerning his wealth if he has no heir other than the disorganized public treasury, so that it may be spent in obedience to Allah after his death. Based on this, it is not permissible for someone other than the owner of the money to make a legal stratagem to divert it from the disorganized public treasury, just as it is not permissible to do so if the public treasury is organized. Therefore, the legal heir of this woman is the public treasury, and forging documents for this purpose is not permissible. You can inform the officials of the truth of the matter; perhaps they will leave the house to you.