I think the question is - someone outside the US has a business, moves to the US on an H1B, and wants to continue working for their outside-the-US business.
Sorry I meant working inside the US for company registered outside the US
(You misread)
US immigration law hasn't caught up with remote employment but the short answer is no and this makes sense since this would allow anyone in the U.S. to circumvent U.S. immigration law simply by setting up an entity outside the U.S. and then getting paid by this entity.