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Thank you, great guru! now the question is: will I have any problems if I travel abroad and re-enter the US while my original I-94 is still valid ? Will this H1 transfer be confusing to the immigration officer at the port of entry?

I'm currently working for the Company A. My I-94 is valid till October, 2007. Some time ago I got an offer from Company B and they applied for H1 transfer for me. My wife and a daughter (both have H4 visas) were also included into the petition. The problem is that I changed my mind and don't...