Here is the details too - so we do not even need a new I20 in my opinion right? 

F-1 academic students on post-completion OPT maintain valid F-1 status until the expiration of their OPT. Once that OPT has ended, they are authorized to remain in the United States for up to 60 days to prepare for departure.
* Under this rule, the F-1 status of students is automatically extended when the student is the beneficiary of an H-1B petition for the next fiscal year (with an October 1 employment start date) filed on his or her behalf during the period in which H-1B petitions are accepted for that fiscal year.
* The automatic extension terminates when USCIS rejects, denies, or revokes the H-1B petition.
* If the H-1B petition filed on behalf of the student is selected, the student may remain in the United States and, if on post-completion OPT, continue working until the October 1 start date indicated on the approved H-1B petition.
* The student may benefit from this provision only if he or she has not violated his or her status.