same situation, Vermont Center

I got the copy of the letter from DOS on Jan 30, haven't got any response from INS.

Your university can submit your H-1 application to INS. Anyway, you have to submit your H-1 application before your J-1 expiration data, or else, you will be out of status. If INS needs your J1-waiver final approval, they will request for your evidence. They may issue your H-1 visa without final approval if you are so lucky.