immigration law, N400 form

Misrepresentation of material facts is a lifetime basis for the government to revoke whatever immigration benefits the applicant receives from the application containing the misrepresentations. The government likely will assert that truthful information about your marital status and your wife is material.

If your wife visa requires her to be outside the US, she likely would need to fulfill that obligation or get a waiver before she can adjust status when you become a citizen.

If you are truthful about your wife and her location, the enforcement arm of the immigration service (ICE) may get involved. However, given the lack of the government's resources, there may not be any active enforcement against your wife specifically.

You likely should review your facts with an attorney before sending in that application.

An immigration attorney should be consulted as there are a number of details that make a difference to this case and options available to you and your wife. For example, do you know if your wife is subject to the two year home residency requirement based on her J-1 visa? Further, if she is then there may be a waiver available although it may be difficult to get in this case. This would in turn affect whether she would be able to get another visa to re-enter if possible.

It is very important to realize that committing any sort of immigration fraud can have severe consequences so you want to avoid that at all costs. In addition, it is important to know that if a person is unlawfully present in the U.S. in unlawful status for between 180 days and one year, and then they attempt to re-enter the U.S. at a later time, they will be subject to a 3 year bar. If they are present in unlawful status for over 1 year then the bar is 10 years. These are just some basic immigration insight and are by no means advice, you should speak to an immigration attorney.