Yes you are right. At least it WAS.
I have changed my status from J1 to H1 five years ago.
2/2000 get waiver
4/2000 H1b application sent out
4/20/2000 J1 expired
5/20/2000 J1 grace period expired
6/2000 H1b application apprived
10/2000 start my new job
(due to quota for 2000, I have to wait until october to work)