What is the ruling on a person impersonating another person in general, and the ruling on an unregistered person impersonating a deceased person to obtain their citizenship after the deceased's will and the family's approval, in order to achieve permissible benefits such as the impersonator's children obtaining identity cards that enable them to study, marry, and find employment?

The default is that it is forbidden to forge a name, because it is forgery and claiming a lineage other than one's father. The Prophet, peace and blessings be upon him, warned against false testimony and claiming lineage from other than one's father. It is not permissible except out of dire necessity, such as someone who cannot obtain their rights or the rights of those they support in work, education, or marriage through legitimate means except by forgery. The sin for this falls upon the one who compelled them to it. It must be limited to the extent of the necessity and one must be wary of anything that could lead to embarrassment or affect rights, such as inheritances.