I think it's the case with TN to green card transition, which is also technically possible but lies in legal grey area. As far as I understand TN-1 to H1-B is

I think it's the case with TN to green card transition, which is also technically possible but lies in legal grey area. As far as I understand TN-1 to H1-B is a straightforward and above the table process: my employer's lawyers OK-ed all my trips and didn't warn me about any potential complications on the border. But again, do not take it as a legal advise, I'm speaking from my limited personal experience.