Got valid H1 and L2 Stamping. Currently I-94 on L2. How to get I-94 on H1?

[BuzzV]

I am on L1 Visa. My wife is on L2. We are currently in California. She also has a valid H1B stamping in her passport.

All along she was on vacation. She has now got a job through H1.

Please let us know the procedure to get a I-94 through H1. Which of the below options would work? Is there a better option?

1. She travels out of US and comes back using H1 stamping. In this case, will travelling to Mexico border and returing immediately help?

2. Go to the nearest US airport immigration and get a new I-94 using the H1 stamping.

[txh1b]

1 will work. 2 will not work.

[kabkaba]

Her new employer needs to file a new cap exempt petition for her. I understand she is in L2 status right now, which is determined by her latest I-94. Once that is approved she can enter using new petition approval notice and the same H1 visa stamp.
Also, the new petition itself can have a automatic COS application included, in which case new H1 I-94 will be attached to the petition approval notice.

If she is joining the same old employer who filed her original H1, then she will need current job offer letter (with current date) to enter on that visa and old petition approval notice.

[BuzzV]

She is joining thru the same old employer. We have the offer letter and old petition.

Is travelling outside the country and rentering the ONLY option?

If so, which country is the best? Canada or Mexico and some other country? Is travelling by road and flying to the country the best option? Pls advice.