AC21 notification

I am working for a company with EAD. My I-140 has been approved long time ago and I am waiting for I-485 to be approved.

Now, I want to change an employer based on AC21. Does anyone know whehter I should inform the CIS the change of employer? I consulted two lawyers, one says I'll have to and another one says I don't have to. Both lawyers are Americans and have many years of experience. I am so confused.

Thanks in advance.