Given
FCL.905.FI FI — Privileges and conditions
The privileges of an FI are to conduct flight instruction for the issue, revalidation or
renewal of:
(b) class and type ratings for single-pilot, single-engine aircraft, except for single-pilot high
performance complex aeroplanes; ....
and
FCL.905.CRI CRI — Privileges and conditions
(a) The privileges of a CRI are to instruct for:
(1) the issue, revalidation or renewal of a class or type rating for non-complex non-high
performance single-pilot aeroplanes, .....
I think it is ludicrous to state
There is no such thing as cri privileges for FI
or
FIs do not have CRI privileges