While it might be "possible" it won't be easy AT ALL and it would be very expensive.
You'd be dealing with US and German and likely EU gun laws, and all kinds of international regulations, fees, taxes, and permits and shipping restrictions.
With all that, there's a good chance of the gun getting "temporarily" seized coming and going in each country until the paper work gets investigated to insure its all legal and properly filled out.
In any case, you personally can't ship it at all. It'd have to go through a dealer that has a FFL license, AND is legally set up to ship firearms internationally.
Best advice, forget it, and send the gun to the US repair facility. That costs enough as is.