I've been looking into earning the CFI-SP. I was ready to give an opinion, then decided to read Part 61, yet again. I thought a CFI-SP could only give instruction in an airplane to a Sport Pilot, not to a Private. In other words, if someone wants to earn a Private with airplane rating, they would have to be taught by a CFI, not a CFI-SP. When a Private is mentioned, it's in conjunction with a powered parachute or weight-shift. After reading Part 61 again, it seems vague to me, actually.
This makes it seem that you can NOT give a flight review to a Private::
§61.413 What are the privileges of my flight instructor certificate
with a sport pilot rating?
If you hold a fight flight instructor certificate with a sport pilot
rating, you are authorized, within the limits of your certificate and rating, to
provide training and logbook endorsements for––
(a) A student pilot seeking a sport pilot certificate;
(b) A sport pilot certificate;
(c) A flight instructor certificate with a sport pilot rating;
(d) A powered parachute or weight-shift-control aircraft rating;
(e) Sport pilot privileges;
(f) A flight review or operating privilege for a sport pilot;
(g) .......
***************************************************************
This makes it seem that you CAN give a flight review to a Private.
§61.415 What are the limits of a flight instructor certificate with a sport pilot rating?
If you hold a flight instructor certificate with a sport pilot rating, you are subject to the following limits: proposed flight under the existing conditions and within any limitations listed in the logbook that you consider necessary for the safety of the flight.
(d) You may not endorse a:
(4) Logbook of a pilot for a flight review, unless you have conducted a review of that pilot in accordance with the requirements of §61.56.
So, it looks like an indefinite maybe to me. I'd like to see a solid answer here from someone.
This is slightly related to the current controversy regarding training received for a Sport Pilot cert. If that training is given by a CFI-SP, it doesn't count toward a Private if a pilot wants to upgrade later. Dual received from a CFI during Sport Pilot training would be able to be counted toward a Private cert later. EAA and others are arguing that even training from a CFI-SP should count toward a higher certificate.