Yes he can lodge a complaint.
Here is the logic behind that. . .
Your employer sponsered you for your green card stating that he has a job requirement in the future, and he couldn't find a qualifying candidate here. So ins guidelines are you should stick with that job for atleast 6 months after getting gc. Otherwise they will make you liable for that, saying that you are trying to cheat the system. But again, if you have a strong case, you can avoid complications. The better thing, I think is, after getting gc, ask your employer or make your employer to terminate your employment. That way you can say that you did not want to go but you were terminated. Or leave the employer in good terms so that he won't complain against you.
