How to transfer H1 while I am on OPT?

New Employer has to file new petition for you. Be aware of risks of not being approved, as employer A is likely to cancel their petition...

Is having ties to the US decrease my chances of approval for a B2 (or B1) visa? What's my best option based on the details?

It depends, if you have a history of coming back and forth, not overstaying your visa, and you have a job/family in Europe, you should be ok....

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How to maintain residency?

The best option is to apply and get citizenship. Otherwise, Re-Entry permit, but it's valid for only 2 years.

Will H1-B case abandoned?

It looks like you are better off leaving the country and after H1B is approved, getting an H1b stamp to come back.

I (Canadian) and my American Boyfriend want to get married. What are the possible routes to take?

Get married in Canada and apply for immigration visa.

What forms do we complete for my husband (green card holder)to return to US if he has been out of the country 10 months.

To return to the US, your husband will need to demonstrate that he in fact resides here and how proof: bills, invoices, waiting for him employment,...

Employer's obligation to notify USCIS of my transfer?

You should check all this with the attorney who helped you to get L1 visa.

To find an immigration lawyer in your area you can 1. search this website. 2. search AILA website .2. call local bar association 4. look though...

My sister is a US Citizen married someone who overstayed from a tourist visa.

Yes, he should fill out all the forms truthfully. The unauthorized employment for spouses of the US citizens is often forgiven.

Do I need to wait for my H1b petition to come through before applying for my green card through marriage?

Yes, you may, and should file for your green card based on marriage.