Question: Should my employer cancel the H-1B visa if I get a EAD/AP? I have an approved I-140 and my I-485 and EAD applications were just filed.
Answer: It depends on the circumstances. If the job is going to change after obtaining the EAD, then the H1B should be terminated (or an amended H1 filed) since you are no longer employed at that H1b position.
If you will continue without any material changes in the job, we recommend that the H-1B should be maintained.
As an attorney, I routinely advice clients to maintain their H-1B visa even after the I-140 is approved and the I-485 filed. I recommend renewing the H1 as a backup. Clients should keep extending the H1, if possible, till the green card is finally issued. I understand that it is expensive to extend H-1Bs, but the benefit sometimes justifies the cost. After the I-140 is approved, H1s may be extended for three year terms, reducing the total number of extensions needed (and thereby, the expense). On the other hand, a green card is not a right till it is actually issued. There have been several instances in the past few years where approved I-140s were re-opened by the CIS or the beneficiary had issues adjusting status (shoplifting or DUIs come to mind). In those cases, if the beneficiary has a non-immigrant visa, they have status in the US to stay and work while the green card issues are resolved.