FCL905 Lists the Privileges that may be attached to an FI Rating and includes both Night (e) and IR (g).
An FI(R) is not a seperate or different rating, it is simply that certain privileges of the FI are "Restricted" Those privileges are stated in
FCL.910.FI FI — Restricted privileges
(a) An FI shall have his/her privileges limited to conducting flight instruction under the supervision of an FI for the same category of aircraft nominated by the ATO for this purpose, in the following cases:
There is no mention of restricting the IR privileges if so qualified. I have in the last year encountered two FI(R)s who are qualified to teach the IR.