Happened to us...
Our company has recently been the subject of a similar attack, setting up a fake website with jobs on it, posting job adverts, and inviting people to a 6 week training course with fees of about $2,500, which they promise to pay back on completion. We're UK based, and the fraud made it look like we were branching out into the US and taking people on.
Cue lots of worried Americans emailing and calling us wondering whether it was legit. They'd been sent contracts of employment and all sorts and all seemed to be at different stages through the fraud, from seeing the initial advert, to booking flights / hotels to go to the non-existent course.
We contacted Action Fraud, who appeared to do nothing at all, and we got the website shut down by messaging a very nice Ukrainian DNS provider who were very helpful, but they popped back a week later with the same website, and slightly altered DNS name (they put a hyphen in it). That's now shut down too, and it's been quite for a week or 2 now.