An FI has the right to teach for PPL issue and Class/Type Rating issue, as mentioned in JAR-FCL 1.330 (a). The job advert is misleading if it mentions "FI with CRI", unless it is refereing to the fact you must be an unrestricted FI holder as opposed to an FI(R).
An instructor (FI, CRI, TRI, IRI, SRI, MCCI, STI) can only teach something he holds, so without an IR they would be limited to IMC only.
Hope that helps
smithgd