completely unrelated as in if you follow the transaction graph they haven't crossed paths, so you'd need the mixer log to break the mixing.
It's difficult to know what they do with the coins, but they could be selling them on an exchange to move onto a different currency and then buy bitcoin again.
This sort of thing has been done with actual money, basically forever. It's exactly what forensic accountants are trained to untangle, in cases where far less information is available. It's not going to fool any serious player.
Nobody's bothered doing this yet on any kind of scale, but that is only because major players in the underground Bitcoin space have found other ways to get caught.
getting the information from a tightly regulated bank could be a different story to getting it from an anonymous service on Tor though. They probably don't even store it.
It's difficult to know what they do with the coins, but they could be selling them on an exchange to move onto a different currency and then buy bitcoin again.