This recently happened to me and of course results in the SEs seeing duplicate content.

I've contacted the registrar of the offending domain name (no reply yet) and I've contacted the host of the site-- which happened to be an arm of Microsoft.

They replied first within 12 hours then 12 hours later sent me the link to how to officially register a complaint about a site that was in violation of their terms and agreements.

It wasn't too hard to gather the info, and I did that, over-nighting it to them. Have since received email that they are working on it, but can make no other comment until the issue is resolved.

BUT those are the institutions to go after -- registrar and host.

DMCA
[google.com...]

easy and efficient

Copyright litigation is unfortunately a burgeoning field
I would doubt a major firm would go to court for less than $50k. What you want is for a major firm to write a letter and follow w a phone call and posture. If it doesn't settle, be prepared for a long expensive fight or cut bait