Sounds like a pretty worm/proxy implementation, rather than mere content scraping.
Could be simply software installed on the other server that feed itself through redirected requests through your server. Kind of like a proxy, but with code-changing capabilities that munges the code from your site on the way to make it look "local" to the other site. Pretty easy to code. I use the same principle as a connection on one of my sites to allow a few pages to be indexed that otherwise would not indexed and to get some of the content from a redirected domain to show up in the right place between servers. Unique implementation, but not hard. I also in an earlier life kept source repositories on development sites in the US and India in sync the same way by building software to replicate and filter commands across the net so they looked "local" to our US based repository. Back when we had "slow" private lines between continents. :)
Can you track your server logs? Check if requests land on your site in sync when you click around the other site, and where they originate from. Then block that server/IP if you find it. If it is merely a remote proxy, that IP should show up very frequently in your logs, and should show when you click the remote site. Block in httpd or better in your firewall. But watch, as they might just switch IP and continue running.
Also, in your browser, check the source code of the other site's html pages and check their references to see where they come from. Maybe they are not replicating/filtering everything, but is actually using your server to serve up things like CSS, JS, images, ... Making their server in Germany look much faster. :)
That kind of replication is pretty easy to do.. It is easy for anyone to replicate any web-site anywhere else that way, if the owner is not actively watching logs and requests, and watching who/what is loading from where. But obviously, it would make a LOT of requests seem to come from the same "person" over there in Germany. :)
What you also have to be extra careful about is that if their site is getting indexed into Google (you should check), you will suddenly end up having your own site at risk for being deemed "duplicate" content by the Big-G algorithms, unless Google already know about this scammer and are discounting them. Pick some unique sentences from your site and search for them on Google. See if both you and the other site show up.
Hard to know anything more without knowing what the actual sites are. Especially the offending one.
This is one of the problems of hosting a site with a