Abridged back story: a former sales employee of ours left at the end of Oct on civil terms, after a year of OK (but not great) performance, telling us they were planning on leaving the country to stay with family, and not returning to the industry.
3 weeks later, they have just turned up in an equivalent role with a competitor about 2 miles away. As they are entitled to do.
BUT on their last day with us, they sent an email to their personal mail, with a blank copy of our company headed paper. Then deleted all their sent mail and logged off.
We restore any mail deleted by exiting employees from back-ups as a matter of course, hence why we know this.
Their new employer didn't approach us for a reference. The employee was with us for 14 months, and that they worked with us is well referenced in the public domain. The new employer is a big company, so seems unlikely that their HR dept wouldn't have asked for references. The employee had form for lying to clients (and we are currently clearing up a couple of messes they left behind in this respect, which have come to light after she's left).
Would you ask the new employer if they were given a written reference on our headed paper, purporting to be from us, and if so, let them know it's a fake?