by 'missing from Google' i assume they mean missing from the SERP's. It has long been a black hat trick to mirror a site onto a higher page rank url structure, and by doing this, the original page will be filtered out at the time of search as being the lesser important page. it IS effectively you taking you out of google, as no-one wants to be in the google database, they want to be in the Search results.

I blogged about this a while back Old Welsh Guy The Google Expert » Beating the Content Thieves - stolen website content one of the main things you need to do is file a DMCA report (instructions in blog post).

let them have their copy of the site, but focus first on getting Google to remove them. They are far more likely to respond to a DMCA report than a spam report, as the DMCA report is a legal matter while spam is a quality issue

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