Is it possible to move from h1b non profit to h1b Masters degree quota and not Capt exempt?

Question

I work in non-profit org and have I-140 approved. H1B application says "CAP H1B US Masters degree or higher" in "how this petition should be counted against the H1B cap".

Does this mean my H1B was NOT cap exempt even though I work in nonprofit? 

Can I move to a non-profit organization in that case? Please advice.

Answer 1

Yes, you can change employers and move to another employer who is not cap exempt. You were already counted against the cap once, and thus will not be subject to the cap again.