According to this article on Wikipedia it is very possible that Major Hill was in the United States on the dates you have listed. https://en.wikipedia.org/wiki/IX_Troop_Carrier_Command
Best way to find out service records is through the National Archives at the following link
Best Wishes and Good Luck in your search.
Dear Ms. Lapihuska,
Thank you for posting your request on History Hub!
We suggest that you review the morning reports for his unit. Morning reports for Army and Army Air Corps units from November 1, 1912 to 1959 are in the custody of the National Archives at St. Louis (RL-SL). For access to these records, please contact RL-SL via email at firstname.lastname@example.org.
We searched the World War II Operations Reports, 1940-1948 in the Records of the Adjutant General's Office, 1917-1981 (Record Group 407) that may include records of the 392nd Signal Aviation Company and the 1709th Signal Service Battalion. For access to and/or copies of this/these records, please con. tact the National Archives at College Park - Textual Reference (RDT2) via email at email@example.com.
RDT2 also has custody of microfilm copies of operational records relating to U.S. Army Air Force/U.S. Air Force units. We searched the Air Force History index to the microfilm and located 4 files that pertain to the 392nd. Please read the brief Abstract to determine which records you are interested in and click on the specific PDF icon. In the PDF listing, the IRISREF is the microfilm reel number and note the FRAME and FRAMELST numbers for the location on the reel. Since the reel number begins with A, please contact RDT2 for access to them. No files of the 1709th were located.
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 RL-SL and RDT2. We apologize for this inconvenience and appreciate your understanding and patience.
The U.S. Army Center of Military History has the lineage and honors of the 392nd Signal Company that may be of interest.
We hope this information is helpful. Best of luck with your family research!