Bad idea. Visiting Mexico does not reset the clock or make any difference. If CBP suspects she is abusing her B2 (actually living in the US), then they can revoke the visa and even ban her from the US for years.
That is not what official USCIS documents say:
https://www.uscis.gov/i-9-central/temporary-i-551-stamps-and-mrivs
"When a new immigrant first enters the U.S., U.S. Customs and Border Protection (CBP) will stamp the passport with an admission stamp that indicates the immigrant has permanent resident status"
If your Green card arrives, it means CBP failed to do their job!!!
Please keep us updated.
No. Not needed for an I-134. An I-865 is for sponsors and joint sponsors who who have submitted I-864s only.
I-134s are not really enforceable and are valid for only 90 days after the K-1 visa holder arrives in the US.
That is absolutely inaccurate. There is no such thing as "automatically endorsed". As I stated above, immigrant visas must be endorsed for 2 reasons. They have stopped stamping VISITOR visas, but immigrant visas MUST be endorsed.
We know what we are talking about. That tier 1 rep you spoke to is clueless.
The fact is that all immigrant visas must be endorsed. First, it starts the processing of the actual Green card. Secondly, the date on the endorsement reflects when the temporary Green card expires...i.e., one year.
That means the fee was paid BEFORE you entered the US. It is irrelevant to whether your Green Card is being produced since it is only one of the required conditions. I hope CBP actually endorsed your visa.
According to the OP, CBP never saw his immigrant visa. He thinks the Green Card will be mailed without having CPB processed his entry. Personally, I don't trust the answer he got from the USCIS tier 1 rep.
Actually, you did. Sounds like a lot of people participated in what could be a federal crime since you and the employer knowingly used another real person's SS number for your employment paperwork.