RE:
it varies throughout the EASA member countries.
I have seen a lot of licences and it realy varies.
In old JAR-FCL licences, there was usually only FI(A) rating with no other privileges and IRI(A) rating if the holder was only IRI(A) instructor. If the holder was FI(A), we always had to take a look into his pilot logbook for training and checked the skill tests forms to proove he has passed the JAR-FCL1.330(d) requirement. It was really a big mess in this!
In EASA (PART-FCL) licences, the endorsments varies.
If holder is just IRI(A) holder, it is simple.
If he is an FI(A) holder, there must be specification of the FI(A) privileges. For example Czech pilots, they have just FI(A) endorsment in the licence and separate A4 letter sheet with the detailed privileges, which is called Instructor certificate.
Some other countries, eg Slovak republic they have FI(A) endorsment and also the privileges detailed explained directly in the licence. eg. FI(A) FCL.905(g) EIR(A), FCL.905(g) IR(A)
Some other countries, eg. Austria, they have FI(A) endorsment and also the privileges detailed explained directly in the licence. eg. FI(A) - IR
etc...
if you have any questions, please feel free to ask.