While there are restrictions an individual with an H1-B may transfer jobs even after they've applied for permanent residency. American Competitiveness in the Twenty-First Century Act of 2000 (AC21).
Right. I think (please correct me if I'm wrong) the thing that prevents them from making a transfer is that the green card application gets reset. That could be a multi-year setback in their path to a green card.
Nope, AC21 allows you to transfer even if you have applied for permanent residence. There are restrictions based on where you are in the process and that the new job meets certain criteria.