H1B holder resigned before new LCA approval - is it problematic if last day comes before the new company gets H1B transferred?

You can start working when the I-129 (H1B petition is filed; you don't have to wait for the transfer to be approved. The LCA takes only a few days...

Affidavit of support I-864 & I-864A: I don't have job in USA, but I get retirement pension from origin country ..

These sound like income, since they are periodic payments. An asset is a fixed sum that is already in your possession, like a house or a bank...

After I got guaranteed asylum state of ca can I move to different state looking for batter job or do business

Yes, you can live anywhere in the U.S. Just make sure you register your change of address with USCIS.

You would still have the F1. The change of status from F1 to H1B only takes place if the H1B status is granted, and even then only when you start...

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Can letter from employer be used as proof to meet income requirement?

Yes, but also send copies of all recent pay stubs showing the increased salary, if it is already being paid.

An employer is applying for an extension of H1B for another 3 years for an employee with an arrest record.

It's not needed for the employer's H1B extension. Just for visa renewal when employee goes abroad, or any application for change or adjustment of...

Can a person not drawn in the "H1b lottery" work on OPT in the same Fiscal Year?

The answer is Yes to both questions. Whether your employer's H1B petition fails the lottery, or even if it is rejected, your OPT status will not...

If i get married to my us citizen fiancée can i get a travel document before getting the green card?

Yes. File a I-131 application for Advance Parole along with your husband's petition and your Adjustment of Status application. You'll get a travel...

I am in my case of asylum , my passport is expired . if I want to get married with us citizen do I need a passport ?

This is really a matrimonial law issue. You will need ID, but an expired passport may be good enough. Check with the county clerk's office.

My current H1B visa expires in Oct 2015. What is the latest that I should apply for GC so that I can stay beyond Oct 2015 ?

Your Labor Certification must be filed one year before your six years on H1B is finished.