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It is possible to get your CFII as your initial flight instructor rating. It this were true, then it would be possible to be a CFII and not be legal to give instrument instruction in a single or multi, since you only have the CFII. This would make no sense.
If you only have the CFII your certificate will say:
Flight Instructor
Instrument Airplane
Note that it does not specify what type of airplane. In this case the only rating you could endorse a student for is the instrument rating, although you could provide the instrument training necessary for the commerical certificate as well as give an IPC as long as you have a commercial pilot's certificate for what ever airplane you are instructing in.
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This is what 61.195(c) is for
Look at this
QUESTION: Can a Flight Instructor with only an Instrument-Airplane rating on his CFI certificate (but no Airplane Single-Engine rating on his CFI certificate), and Airplane Single-engine Land, Instrument Airplane ratings on his pilot certificate give the flight training required by § 61.65(c) for an instrument rating added to a Private Pilot Certificate-Airplane Single-engine Land?
ANSWER: Ref. § 61.195(c); The answer is yes as addressed in § 61.195(c).
So in the example in your question, the flight instructor holds instrument privileges for the Airplane Single-engine Land rating on his pilot certificate and also instrument instructing privileges for the single-engine airplane on his Flight Instructor Certificate. Yes, that is what § 61.195(c) means!
In the past, I have heard of an unwritten rumor going around that supposedly said a flight instructor who only held a Flight Instructor Certificate-Instrument Airplane and Commercial Pilot Certificate with an airplane-single-engine land rating and instrument-airplane rating could provide instrument training to an applicant in a multiengine airplane. That practice is not permitted any longer, if it was ever permitted in the first place!
As an example, a flight instructor, who only holds a CFII-A rating is giving instrument training to an Instrument-Airplane applicant in a single-engine land airplane. That flight instructor must hold the following:
Flight Instructor Certificate Commercial Pilot Certificate or ATP
Instrument-Airplane Airplane Single-Engine Land
Instrument-Airplane
Another example. A flight instructor, who only holds a CFII-A rating is giving instrument training to an Instrument-Airplane applicant in an multiengine land airplane. That flight instructor must hold the following:
Flight Instructor Certificate Commercial Pilot Certificate or ATP
Instrument-Airplane Airplane Multiengine Land
Instrument-Airplane
However this example is a “no-no” and a violation of § 61.195(c). A flight instructor, who only holds the following and wishes to give instrument training to an Instrument-Airplane applicant in an multiengine land airplane shall not do so.
Flight Instructor Certificate Commercial Pilot Certificate or ATP
Instrument-Airplane Airplane Single-engine Land
Instrument-Airplane
As per § 61.195(c), which states in pertinent part: “. . . must hold an instrument rating on his or her flight instructor certificate and pilot certificate that is appropriate to the category and class of aircraft in which instrument training is being provided.”