1) an examiner
2) A person authourised by the US armed forces to conduct instrument flight tests, provided the person being tested is a member of the US armed forces.
3) A company check pilot who is authourised to conduct flight tests under Part 121, 125 or 135 of this chapter or subpart K of Part 91 of this chapter and provided that both the check pilot and poilot being tested are employees of that operator or fractional ownership program manager as appliacble
4) An authourised instructor
5) A person approved by the Adminstrator to conduct instrument practical tests.
look at number 4), an authorized instructor can be a CAA instructor too.
I know this is in the FAR somewhere, check FAR61.41 (flight training given by a non FAA instructor).They don't say an FAA instructor, they say an AUTHORIZED instructor.
now check that:
Sec. 61.41 Flight training received from flight instructors not certificated by the FAA.
(a) A person may credit flight training toward the requirements of a
pilot certificate or rating issued under this part, if that person
received the training from:
(1) A flight instructor of an Armed Force in a program for training
military pilots of either--
(i) The United States; or
(ii) A foreign contracting State to the Convention on International
Civil Aviation.
(2) A flight instructor who is authorized to give such training by
the licensing authority of a foreign contracting State to the Convention
on International Civil Aviation, and the flight training is given
outside the United States.
(b) A flight instructor described in paragraph (a) of this section
is only authorized to give endorsements to show training given.
now read the first line, it says" toward the requirements of a
pilot certificate or rating issued under this part".
once the IR student has obtained the requirement toward and instrument renewal, in this case, flying some approaches with a CAA FI, he satisfies the requirement to renew an instrument.
the CAA FI has just to sign and date the "student" loogbook, with the mention "instrument renewal" and the FAA can just accept that, as the student is already instrument certified.
et voila!!!better to ask the FAA, but I bet you will get 36 answers....