according to JAR-FC 2 amendment 3 as per CAA website
A FI(H) may conduct flight instruction on:
2.330 (f) a single-pilot multi-engine type rating, provided that the [FI(H)] meets the requirements of JAR–FCL 2.365 (a), (b), (d) and (f)
AND
2.365 (a) successfully completed an approved TRI course at an approved FTO or TRTO (see Appendix 1 to JAR-FCL 2.365 and AMC FCL 2.365);
AND
appendix 1 to 2.365, Pilots holding or having held one of the following ratings are credited for the TRI(H) Teaching and Learning part of the TRI(H) course:FI(H)
NOTE
(no mention is made of exemptions the technical trainining and flight training parts of the course)
In summary my understanding is that if you are not an FI(H) you need to do an TRI(H) course and if you are an FI(H) you still need to do an TRI(H) course, but not the teaching and learning part, for both there are other requirements regarding validity of ratings and experience etc.
so at this stage I stand by my original post, I never said you had to be an FI(H) before you could be a TRI(H), they are different classes of instructor, but if you are it can give you some credit in the course.
regards
CF