According to an announcement from the U.S. Citizenship and Immigration Services:

"Under Pub. L. 101-249, use this form to request posthumous citizenship for an alien or noncitizen national whose death resulted from injury or disease incurred on active duty with the U.S. armed services during specified periods of military hostilities. Posthumous citizenship is an honorary status commemorating the bravery and sacrifices of these persons; it does not convey any benefits under the Immigration and Nationality Act to any relative of the decedent.

"If we approve your application, we will send you Form N-645, Certificate of Citizenship, in the name of the decedent. The certificate only establishes that we consider them to be a citizen of the United States as of the date of their death, and is invalid for all other purposes."

Details may be found at the Citizenship and Immigration Services website at: https://www.uscis.gov/n-644.