Dear Mr. Citerin,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Records of the 1st Through 338th and the 559th Infantry Regiment in the Records of U.S. Regular Army Mobile Units (Record Group 391) that contains records of the 56th Infantry Regiment and Records of Divisions in the Records of the American Expeditionary Forces (World War I) (Record Group 120) that contains records 7th Division (see Boxes 11-12 for records of the 56th). For access to and/or copies of these records, please contact the National Archives at College Park - Textual Reference (RDT2) via email at firstname.lastname@example.org. We were unable to locate specific records of Company H. Records of lower echelon units sometimes were incorporated into the files of the regiment.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from the RDT2. We apologize for this inconvenience and appreciate your understanding and patience.
According to the Center of Military History (CMH) Publication Order of Battle of the United States Land Forces in the World War, Volume 2 American Expeditionary Forces: Divisions, the 56th Infantry Regiment was assigned to the 13th Infantry Brigade, which in turn was part of the 7th Division. We searched the CMH website and located Battle Participation of Organizations of the American Expeditionary Forces in France, Belgium and Italy 1917-1918, Combat Service of Organizations of the United States Army in the World War, and Service of Major Organizations of U.S. Army Outside Continental Limits of the U.S. During the World War. All of these provide a very brief overview of the campaign credits of the 7th Division.
We also searched HathiTrust and located the books 7th Division Summary of Operations in the World War prepared by the American Battle Monuments Commission, and History of the Seventh division, United States Army, 1917-1919. Obtained from official sources. Approved by unit commanders. .Compiled by Captain Edgar Tremlett Fell. Both have been digitized in full, may be viewed online for free, and are searchable for information about the 56th Infantry.
We hope this information is helpful. Best of luck with your family research!