I have the same situation.

来源: 于 2008-10-03 17:26:30 [旧帖] [给我悄悄话] 本文已被阅读：次

As far as I know, I think the answer is you are legal
to work and don't need to go abroad.

But there is a few restrictions:
1. You must get the receipt before you can work for
the new employer.
2. You must file H1B transfer before your current H1B
expires.

There may be a few other things you can google out.