Nick (et Al)
There are two items which pertain here. 61.41(a)(2) and your definition.
61.41 which says that you can get credit from non-FAA instructors.
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.
However, 61.41(b) is relevant. It says that the instructor can only show give endorsements to show training given. This is as opposed to endorsing for checkrides, practical tests etc..etc..
Wherever the FAR requires a checkride endorsement or similar, it will ask for an 'authorised' instructor, which is per the definition in your post. i.e. FAA certified.
Basically the answer is yes, but the foreign instructor cannot sign-off on anything.
Hope this helps.
cl12pv2s
P.S. Your solo hours are recognised, by virtue of the fact that it wasn't training....if you flew solo, you flew solo!