There could be issues.
What did Company C's immigration lawyer tell you?
He/she is a 'key' person to talk to as he/she will be providing your wife with the needed documents.
Whatever you do, don't waste time talking to non-attorneys in HR.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
There could be issues at the port of entry. You would be best advised to discuss the matter with your employer's immigration attorney. This attorney should have all the relevant information to address your questions and can also provide you with the necessary supporting documentation.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter. No recipients of content from this answer, clients or otherwise, should act or refrain from acting on the basis of any content included in the answer without seeking the appropriate legal or other professional advice on the particular facts and circumstances at issue from a licensed attorney. Provision of information on this website does not create an attorney-client relationship between you and The Law Offices of Grinberg & Segal, P.L.L.C., nor is it intended to do so.
You should call your employer's attorney to discuss your spouse's H4 situation and entry into the US. The employer's attorney knows all of the facts pertaining to your case and is in the best position to advise you. Good luck!
This answer is for informational purposes only and should not be construed as legal advice.
You seem to be a valuable addition to the American company with your professional talents of prospective contribution since it kindly sponsored you, therefore, ask the employer to kindly direct you to its attentive and considerate immigration visa counsel who will dispel your confusion momentarily.
DISCLAIMER The answer given above by the lawyer serves for educational purposes only and provides general information and a basic understanding of the applicable law. Take notice that the answer above does not create an attorney-client relationship as this website is not intended to provide anyone a specific legal advice. Anyone using the site expressly consents that there is no attorney client privilege between any person and any attorney responding. Further take notice that the site should not be used as a crude substitute for any professional and competent legal advice by a licensed professional attorney in the applicable jurisdiction. The attorney above attempted to provide competent professional opinion, however, the law and its applications may change frequently and vary greatly from other U.S. jurisdictions and locales. Therefore, any information and opinions stated above are general in nature, and may not apply to specific factual or legal circumstances related to one's current legal issues. Contact an experienced lawyer admitted to practice in your State under an attorney-client privilege to further receive a comprehensive legal before making an educated decision about your particular legal issue. Respectfully, Attorney Alexander Ivakhnenko, Chicago, Illinois