35 years instructing here, but no idea what TAE theory is? I believe they are referring to CERT IV in Training and Assessment - used to be TAE 40110 which was superseded by TAE 40116 and now is TAE 40122
Ah OK I have done one of those.
The good news is that if they can't find work instructing then at least that qualification can be used in other fields. Or is it some flying instructor course specific one?