For most visa categories, you need advance parole from U.S. Citizenship and Immigration Services (USCIS) to travel internationally if you have applied to become a lawful permanent resident (LPR) through adjustment of status in the U.S. See the explanation from the government website (customs and border protection) on this topic at https://help.cbp.gov/s/article/Article-991?language=en_US
Failure to obtain travel permission could mean that you have inadvertently abandoned your application for LPR status if you traveled before receiving it in the US.
There are three limited exceptions to the requirement for non-immigrant visa holders to apply for advance parole. One important exception for business travelers is that under 8 CFR §245.2(a)(4)(ii)(C); their AOS will not be abandoned but their initial AP that was filed w the AOS will if an individual in H1-B or L Status travels without waiting for the approval of a pending advance parole (travel permission). Renewal AP applications don’t get abandoned if the person on H or L travels while AP is pending.
According to the CBP website, those “here in H1B, L and K3/4 status – and their dependents – do not require advance parole to travel after applying to adjust their status. K1/2 visa holders who have married a U.S. citizen must apply for LPR status and advance parole prior to international travel”. What the government website does not clearly emphasize, is that it is the responsibility of the individual to print out their I-94 for each entry to the US and keep good records of all entries and departures to and from the US, as the government records are often inaccurate and only the latest entry date can be corrected in the system.
This all matters because under INA 212(a)(9)(B) – erroneous determinations can be made that an individual has accrued unlawful presence for more than 180 days even when the applicants were in possession of valid I-94s during their stay. These findings are made after determining that the applicant may have violated previous nonimmigrant status (e.g., by engaging in employment while present in B-1 or B-2 status). The FAM states that unlawful presence occurs when an “alien is present in the United States after the expiration of the period of stay authorized by the [Secretary of Homeland Security] or is present in the United States without being admitted or paroled.” Accordingly, applicants who violate their status do not automatically begin to accrue unlawful presence.
For individuals filing a Form I-485 to Adjust Permanent Resident Status or to Register Permanent Residence, USCIS requires you to submit a copy of your official stamped passport to and or your latest form I-94 to prove your last lawful entry into the United States. According to the CBP article, “this can include a copy of the official admission stamp in your passport, a copy of the I-94 you received, or the print out of your I-94 number from CBP.gov if you entered after April 30, 2013 and did not receive a paper I-94”. What is not said is that due to potential inaccuracies in the I-94 system, you could be mistakenly thought to have entered the US illegally or overstayed your authorized status simply because government records are inadequate. Or your name could be so common as to cause alerts meant for another person!
If you are a Canadian citizen, and were not issued one upon entry into the United States, you may go to a Deferred Inspection Site (DIS) to request one.
Alternatively, if you have no documentary evidence of legal entry, you may file a Freedom of Information Act (FOIA) request with CBP to obtain your most recently recorded date of legal entry into the United States. To facilitate your request, you should provide the date of your most recent entry, as best as you can remember it. USCIS may require additional documentation after the initial filing of your Form I-485. It is also possible to file with USCIS for a duplicate I-94 using form I-102, however, the processing time can be lengthy, especially with very old entries to the US, which may not be digitized.
That said, it is always to your benefit to maintain your own good records of your trips to and from the U.S. and contact a qualified immigration attorney to clarify the requirements.