Let me first thank you for your replies.
This is the quote from Murthy link:
Previously Approved Advance Parole
The USCIS stated that if a person has an advance parole and applies for a new advance parole while in the United States, s/he may travel and reenter the U.S. using the already approved advance parole. The person must return during the time period permitted under that advance parole that was approved before the person's departure. The USCIS specified that the person cannot remain abroad after the expiration of the first advance parole and then seek to enter on the second one after it is approved.
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So this is for the case when someone has an advance parole and leaves US. My wife won't stay outside US beyond the expiration of AP. Her application is being processed while she is out.
The same link states explicitly that an AP that was not approved before the alien leaves the US cannot be mailed to the alien for use to return. In your wife's case, this is a moot point, since you say she already has a dual intent visa, so it really doesn't matter if she has an approved AP or not, if I understand correctly.
This the quote from Murthy:
Case Example with Dates
A person has an advance parole that is valid through June 15, 2004. S/He files for a new advance parole on April 15, 2004, while in the U.S. On April 20, 2004, the person learns that s/he must travel abroad immediately. Under the USCIS advisement, the person could leave the U.S. and reenter on the first advance parole through the June 15, 2004 date. The advance parole filed on April 15, 2004 will be valid once it is adjudicated for travel from its approval through its validity date.
It would not be permissible for the person in the example above to depart the United States on April 20, 2004 and remain abroad past June 15, 2004, waiting for the second advance parole in order to reenter the U.S. The person could not have someone send him/her the April 15th advance parole in August 2004 and use it for reentry.
My understanding:
The quote from Murthy link is also for the person who has an advance parole and leaves. Then he has to enter US before the expiration of the first advance parole and can not come back with the second one.
Since your wife is arriving on a dual-intent visa, she is eligible to apply for AOS (i.e. I-485) without really arousing suspicion. People entering on strictly non-immigrant intent visas such as B, F, or J would arouse this suspicion. So as long as she is physically present in the US on the day the application is received by USCIS, she should be okay to apply.
The rule says she can apply for AP and leave US and the application is not abondoned because she left the country on L1. She can come back using her L1 but nowhere says that she can not use AP after the approval.
Now the question is if she loses here job in Canada and can not come back using her L1, can she travel back to US with AP.
This is different from the case that someone is outside of US and AP is expired.
I am concerened about it, because lay offs are possible in the time frame of 6-7 months.
Do you see the point that I am trying to make?
My wife's case is not listed neither in AILA nor in Murthy link.
The only thing they say is: she can apply for AP , leave US on L1 and 131 application is not abondened.
So if it is not abondened, once it is approved, based on what rule they can deny her admission?
The whole point of the argument you had was for someone who stays outside US after the expiration of the first AP. My wife's case is a bit different.
With so many thanks to you for the discussion.