Here is a brief on the location of the H/HQ Sqn. of the 39th Service Group.It should only be read as an indicator as to which Air Force the 352nd Service Squadron was attached to.A Group was made up of several Squadrons, so it is likely that the 352 Squadron was stationed at a different air field nearby the Headquarters location.
It is likely that the APO in the return address you provided would be the location of the HQ, as mail was reposted to individuals from Headquarters postal facilities.
"Stalag" who posts frequently on this site is a wizard at decyphering APOs for location.
It is essential in any further research that you utilize the word SERVICE in the search.Otherwise you will incorrectly acquire information on the 39th or 352nd Bomber, Fighter, Troop Carrier....Groups and Squadrons.
""39th Service Group Headquarters and Headquarters Squadron Arrived at Firth of Clyde 6 October 1942 (sailed from New York) [one officer as rear detachment arrives Belfast 25 November 1942 having sailed from New York later] Assigned to Eighth Air Force 9 October 1942; further assigned to 8th Bomber Command 13 March 1943 and to VIII Air Force Composite Command 20 December 1943 Initially located in Bedfordshire and Cambridgeshire in England. Moved to Mughaberry per 20 December 1943 movement order. At Harrington, Cumberland, by 31 March 1944
USAAF personnel at Station 113 (Cheddington) served in the 39th Service Group during 1945.""
My name search resources did not immediately turn up anything regarding Zay B. Smith in a shoot-down or air accident, but I have a few other sources to check.