The simplest way to stop it? Actually email or request transcripts from the uni that ft alleges to have a degree from?

Yes, you've solved the problem rather easily. You deserve much praise.
The foreign teacher would have to do it, not the employer. It should be sent by EMS, and the foreign teacher can open the EMS folder for the first time with the FAO present. University matriculation offices in the west are efficient and can do it in a couple of days. Then by EMS to China, at most 7 days.