I still think you need to send it right away. It may take a couple of days for it to reach there, then their mailroom may take a couple of days to process it, then there may be a weekend. By the time it reaches the officer's desk, it may already be July 1st. Even if it is not, he/she may clear it and put in the line to be approved on day 1.
Are you afraid that they will approve it before July 1 and then you will be in trouble?