All relevent training given by a rated instructor in an ICAO country is recognised as towards the issue of an FAA licence. Similarly, all logged time counts towards the minimum experience requirements. A slight catch though: Only FAA instructors may give certifications if a certification is required. For example, if you fail part of a flight test and must undergo remedial training prior to being retested then the instructor is required to certify in your log book that you have completed the training and reached the required standard of skill.