Is it permissible to reside with someone who previously cheated on immigration requirements to obtain residency and submitted their papers to the consulate to prove their ability to host?

There is nothing in the situation of this person that prevents one from staying with him. His deceit is his own responsibility.

The questioner should be concerned with the ruling on traveling to disbelieving lands for residency. It is not permissible except for one who can observe the rituals of his religion and is safe from temptation. Residing in Muslim lands remains preferable due to the great dangers associated with residing among disbelievers.