Ah, thank you for your very fast reply. I was just concerned due to this thread:

http://www.expertlaw.com/forums/showthread.php?t=105156

where someone advised

You may not work - even for an employer in another country - when physically present in the US without work authorization. Your employer is a US company; that makes it an even bigger issue. You may not do as you are proposing and continue to work.
Thanks again for your new info ^_^