Hiya laakdown,
“… somebody told me that when a JAA student goes to instruct in America …” – I assume you mean that “…when a JAA licence holder with an FI rating goes to instruct in America …..”
From my knowledge, any hours you fly as an Instructor would be valid, though you will have to get an FAA licence and an FAA FI rating to instruct the FAA syllabus. Indeed, from my understanding, the only question revolves round the differences between the way the FAA and JAA deal with "hour building" flying where two PPL hire an aircraft and burn holes in the sky. You would need to check that out but I believe the difference is that, under FAA rules, both pilots can log the time hour building but, under JAA rules, only the handling pilot can claim the time. This assumes that the aircraft being used is a single crew aircraft – which all the usual PPL hire aircraft (152, 172, PA-28, etc, etc) are.
All your "Instructional Hours" as an FI should count as "In Command" no problems. Indeed, from my understanding, most airlines like Instructors. Lets face it, after 1000+ hours Instructing + all your training hours + any PPL P1 time, you will have significant experience over and above an Integrated student straight out the box. After all, they have not have had the pleasure of salvaging aircraft from the weird and wonderful situations students sometime place an aircraft in when trying to devise yet another, even more imaginative, way to kill you! Also, airlines in turn need Instructors so, to have a pool of people who have basic Instructional Technique experience, is also a plus when it comes to selecting future TRIs/TREs. I’ll not enter a “good instructor/poor instructor” debate here! Another topic that is all together.
If anyone else knows different please shout as this is just based on my experience. Personally, Instructing is where I’m heading back to! Clearly, I miss that “my life flashing before my eyes” experience which you don’t get Line flying – generally!!!! I must be mad but I can’t wait!!!!! Hope this helps.
Regards, H 'n' H