Road to a green card

[hds]

I had one year left on my second H1B when I got laid off. I returned back to Canada with my perm address in Canada. I have gotten a new job in the USA and they have agreed to sponsor me for a Greencard. I asked a question on here before if I could still use my H1B for the remaining year and was told I could. However, the lawyer at my new job says that when I left the USA my H1B was cancelled. Is this correct? Also, now they want to put me on a TN. I was under the impression that you cannot apply for a greencard from a TN? Is that true as well.

Thank you for your help.

[immihelp]

I don't see any reason why you can't come back on H1 visa.