Just as a follow up on this.
The owner of the gun did some research and found discharge paperwork from her family member dated 1945 that lists the firearm as "Captured Enemy Material" and authorized the possession of the firearm to the returning GI. So that was cool.
She also found an appraisal doc that indicated it was a Commercial released firearm (as opposed to Military Issued). What this means is that the gun was purchased directly by a German Soldier rather than issued by the military. Generally speaking only specific people could purchase firearms in pre WWII Germany (Officers in the military being the most common people to purchase commercial firearms).
This matches the research I did as well.
So in summary:
-Commercial firearm with a Mfg date of 1939
-Manufactured in ULM Germany
-This is a confirmed GI bring back, with the authorization form from 1945 intact listing it as "Captured Enemy Material"
-Value would be 1500 to 2000 depending on condition
Fun research project!