Hi Steven,
Question is somewhat tricky. Direct linking of FI document to a background job is not always reasonable.
Here is what I would do if I had similar question and if I was sure that FI doc was posted by background job – SM20 and SM37.
-take user name from FI doc header, note ENTRY date and time
-check log via t-code SM20 for this user and noted date narrowing time to noted above, paying attention to lines in log with terminal column EMPTY (those are programs executed in background)
-If no entries in log WITHOUT terminal for given date (and may be within reasonable time range) then it was NOT posted in background
-If you can find some entries without terminal then take programs which were executed closely to the noted time and search for jobs in t-code SM37 narrowing by date, user and program
Best of luck in your search.
Anton