I guess that you will find some differences between the countries, depending on the FCL2 amendment implemented.
The CAA website displays the 3rd while JAA are at the 6th (wich by the way is less complicated when it comes to FI privileges
).
I hold a current FI(H) rating with privileges of instruction on multi-engine helicopters (TwinSquirrel and Puma) although I never attended a TRI course, but that may be because I already was an instructor before the FCL2 got implemented in my country (some kind of "grand-father rights").
Camp Freddie, your last post is right.
It's the first one that triggered some answers (when you said <<.
..the FI(H) is restricted to Single pilot single engine types...>>).
Vertolot,
I think your question was more like (to take some examples) :
<<I have R22 and AS355 ratings.
I have a FI rating with R22 privileges only.
Can you do my FI renewal/revalidation checkride on a AS355 ?>>
I would answer no.