Many employment based green card applications are processed while an applicant is on an H-1B visa. This usually involves filing an I-140 petition along with an I-485 petition. You can find out more about the green card process by clicking here.
When the I-485 petition is filed, an applicant can also file an application for work authorization (EAD) and ability to travel (Advance Parole). Once the EAD has been approved, the question comes up as to whether the applicant should continue to work for his/her current employer on the H-1B or whether he/she could/should work for other employers using the EAD. Specifically, many ask: Can I quit my current job and start working at another employer while my I-485 is pending? Should I work on my H-1B or my EAD while my I-485 is pending?
Technically you can use the EAD card and start working anywhere but once you work outside of your employer (where you are working based on your H-1B), you will no longer be in H1B status and you would only be permitted to remain in the U.S. on the basis of the pending adjustment. You would be able to travel with your Advance Parole card at that point. Generally, it is better to keep underlying status whenever possible as if the green card application was denied for some reason. If you have maintained status on your H-1B, this would give you the option to remain in the US, whereas if your I-485 is denied and you had no underlying status, you would have to leave right away.
