Is the money acquired for work provided to a governmental entity—by submitting a forged invoice implying that the work was done by an external party—lawful or unlawful?

This money is unlawful (haram) because it is impermissible to take it except in specific cases: either it is part of your original job duties for which you receive a salary, or it is a known bonus approved by the state for those who perform this work, or it is outside your job duties and the state has not designated a known bonus for it, or the state authorizes you to take it and you are known for working for wages. In all cases, it is not permissible to resort to deception or lying to obtain money, and what was taken unjustly must be returned.