Your response to 杞子 confused me. I thought she is also transfering from F2 to H4, not the other way. Also, I thought she said her I20 expires before her H4 becomes valid, same as mine. What is the difference you see in her case, that makes her case OK and not mine?
BTW, I also filed my H4 before i20 expires, and it was approved after the I20 expired, but before H4 became valid.
-Then, you are OK too. Just provide the H4 applicaiton receipt and the h4 approval notice and explain in the response letter that you had filed the change of status (I-539) applicaiton on what date before your F2 expired and thus, you were legally present during the change of status application was pending from what date (recipt date on your receipt) to what date (the H4 approval date). Nothing else needed to do!