What is the ruling on a wife obtaining an official, albeit inauthentic, marriage certificate to enable her to travel to her husband, knowing that she is lawfully married to him but consummation has not yet occurred, and the husband justifies this by saying, "Deeds are by intentions" and "The end justifies the means"?

Cheating, forgery, and a woman traveling without a mahram are all forbidden things. It is not permissible to forge a marriage contract in the name of the husband's cousin, because it is forbidden, and this man might claim that you are his wife. Your travel with him could lead to an unlawful seclusion (khalwa). The solution is to be patient until the husband obtains a visa for you.