Though this was okay and common in the past, the FAA has recently clarified that if you only have a CFII certificate, you can't teach anybody anything.
That's not quite true. The holder of a CFI certificate with only an Instrument-Airplane rating (CFI-IA) can give instrument ground instruction and instrument training in a flight simulation device -- just no flight training without also having the appropriate aircraft category rating (ASE or AME).
I would also point out that people often use the term "CFII" as though it were a separate ticket from a "CFI," and that a "CFI" is someone who can give flight training in an airplane. That's not correct, and confuses the issues. See 61.5 for details, but what we're discussing are the various ratings you can get on a Flight Instructor certificate, which include both aircraft ratings and instrument ratings. For example, my CFI certificate has three ratings: Airplane Single Engine, Airplane Multiengine, and Instrument-Airplane, which would best be abbreviated CFI-ASME-IA. Each rating carries with it specific privileges, and an understanding of this system is required knowledge for a CFI applicant, regardless of what rating is applied for with the initial issuance of a CFI certificate. The key is that while you can give
some instrument training with only an instrument rating on your CFI ticket, you cannot give any
flight training (i.e., training in an aircraft in flight) instrument or otherwise without
also having the appropriate
aircraft rating on both your CFI and pilot certificates.
Personally, I think the FAA was silly to allow people to get an instrument rating (e.g., Instrument-Helicopter) on a CFI without already having the appropriate aircraft rating (e.g., Rotorcraft-Helicopter) on that CFI ticket, as opposed to the way they do it for pilot certificates where the appropriate aircraft rating is a prerequisite for an instrument rating, but that's what they did, and it created apparently endless confusion.
