I'm working with Company A and my I-94/ H1B visa is expiring by Sep 17th, 2010.
Company A filed for an H1B extension through regular processing.
----It seems H1 extension is still pending.
Another company
(company B) is willing to hire me.
Should Company B be filing the H1B extension/transfer
before Sep 17th?
------Yes the can before Sep 17th or you need the H1 filing receipt so that new lawyer can write on cover letter that your H1 Ext is still pending from A. Do you know if the H1 Extension from A gets denied due to any reason what will be your status? Do you know that company B H1 will be will be approved? FYI at this time USCIS deny many H1 petitions or ask lot of documents from companies (They check the past record of company if they kept any H1 holder on Bench or not paid or any complaint against employer is pending with DOL.)
If you really want to join B then let Company A H1 Extension get approved and get the H1 extension in your hands keep working with A and let the B file H1 transfer(no need to inform A when B file H1)through Premium processing and once B H1 gets approved then join B. Did company A filed first step of GC that is LC?