Good question!
The issue is whether or not the individual is not "prohibited by law from possessing a firearm", I think, as carrying in a vehicle under your control requires that
specifically (and some other requirements -- let's assume the employee isn't engaged in criminal activity, or a member of a gang :) This requirement, specifically, is PC §46.02 (a-1)(2)(B).
The answer may be found in the document "Questions and Answers - Revised AFT 4473 (April 2012 Edition) located here:
http://www.atf.gov/files/firearms/faq/n ... iens-2.pdf" onclick="window.open(this.href);return false;
Q3. May a nonimmigrant alien who has been admitted to the United States under a nonimmigrant alien visa purchase
or possess a firearm in the U.S.?
A3. An alien admitted to the United States under a nonimmigrant visa is not prohibited from purchasing, receiving, or possessing a firearm if the alien falls within one of the following exceptions: (1)
is in possession of a hunting license or permit lawfully issued by the Federal Government, a State, or local government, or an Indian tribe federally recognized by the Bureau of Indian Affairs, which is valid and unexpired; (2) was admitted to the United States for lawful hunting or sporting purposes; (3) has received a waiver from the prohibition from the Attorney General of the United States; (4) is an official representative of a foreign government who is accredited to the United States Government or the Government’s mission to an international organization having its headquarters in the United States; (5) is en route to or from another country to which that alien is accredited; (6) is an official of a foreign government or a distinguished foreign visitor who has been so designated by the Department of State; or (7) is a foreign law enforcement officer of a friendly foreign government entering the United States on official law enforcement business.
I've set the important points in bold. I would suggest that possessing a valid, unexpired Texas Hunting license will serve to allow the Employee to legally possess a firearm, and thus carry in a car pursuant to the stipulations of PC §46.02 (a-1)