863221 pls

I was and am holding a lower position like research technologist. Company applied perm several years ago for me and I got my greencard and I still hold the old position title. In perm application form, the position they put here was a higer position like research associate. My question is: does the company has the obiligation to offer me the higher position or it is optional to them by law, after my greencard was approved?

Thank you so much,