Frankly, I do not know if one should work for B from SD. In this case, I suggest you contact the both A and B to make an agreement. I guess you did transfer yourself, and you did not notice A yet.
Just be sure A will not terminate too early when you are not ready to serve for B. Also, whenever you receive INS notification before 01/01/05, you should be qualified to work for B, and you do not have to wait for the approval of the case. In another word, in "case" that the case be denied, you could not stay with A either---so nothing is safe. Fortunately, absolutely most H-1B transfer cases (comparable between A and B) are safe, that is it.
Never be troubled with A! Take care.