I got my J1 visa in 2010 (no 2-year rule). I have been working for the same employer since then renewing my J1 every year. In 2011 I renewed my J1 and the immigration officer checked the 2-year rule . In 2012 I renewed my J1 with no 2-year rule. However since 2011 I have had the 2-year rule on my visa on my passport. Recently I was offered a position from the US gov and they will transition me to H1B. They told me that I have strong chances to get the H1B. I personally doubt that. Unfortunately they are not offering an IGA waiver (too complicated to explain here). In any case, I have 2 simple questions: a) What are my chances? b) Is there anything I can do or they can do before the H1B application to guarantee a success? Thanks in advance!If I get the H1B can I apply after that normally for a green card through my marriage with a US citizen ?