It is my understanding that under JAA to teach for the IR the holder must have a current IR and have an IRI rating. The IRI rating can be added to an FI or a CRI. An ME IRI has to be added to the ME CRI rating. An FI who wishes to be an ME Instructor has to do a ME CRI which is what the LASORS entry refers to.
For an FI to teach for the IMC they are required to have the no Instrument flight restriction lifted. It is my understanding that lifting this restriction only allows them to teach for the IMC. An IRI may teach for the IR if they hold a current IR and the IMC. If they do not hold an IR then they may only teach for the IMC.
That is my understanding. I too stand to be corrected.
But the purpose of my post was to point out that there is such a thing an IRI rating, with a course and a test.