Is a Muslim helping another Muslim obtain a residency certificate proving that he lives with him, while he does not reside in the country, considered cooperation in righteousness and piety, or deceit and bearing false witness?

It is not permissible to lie in order to facilitate residency in a non-Islamic country, because that is not a praiseworthy form of cooperation; rather, it is cooperation in sin. A Muslim does not lie or falsify except out of dire necessity, and obtaining residency papers is not considered a necessity that permits lying. Furthermore, a Muslim residing in those countries has given their people a pledge of security by respecting their systems and laws.