Please help with faux artillery (long) Luger

[Milsurp Collector]

I recently bought this pair of Lugers as shooters. The standard one is a 1914 DWM that is matching but has been refinished. The other one is an odd faux long Luger. It is marked Erfurt but there is no date. There are multiple "Germany" stamps so I assume it was imported in the 1920s. The long barrel and sight are completely free of serial numbers. Several parts have been restamped to match. It doesn't have the receiver notch for the rear sight but it does have an artillery toggle that has been renumbered to match.

My question is, is it likely the new barrel was installed in Germany before it was exported, or more likely the barrel was installed in the US?