What is the ruling of Islamic law on receiving a monthly grant that requires signing documents claiming unreal external travels for the administration, and what must be done to atone for the months during which this grant was disbursed?

It is not permissible to sign documents that claim to have made external trips which did not occur, because this involves lying and deception. The Prophet, peace and blessings be upon him, said: "Beware of lying, for lying leads to immorality, and immorality leads to the Fire," and "Whoever deceives is not one of us." If the funds are a grant or a right, they must be disbursed in a lawful manner without devious methods.