Hi Roger Jones,

I understand that you want to transfer your mailbox from OLSB to Office365, and you success verified on office365.But you can’t  access your old mailbox.
Which domain name you are using for email address suffix? If your email address ends with @live.com, @hotmail.com, or @msn.com, emails will not be deleted after transferring to Office 365. You will still be able to use Windows Live (Hotmail) to access, send, and receive email.
However, if you have an email address based on a custom domain, please refer to steps in self-transition guid to move emails for users to Office 365.
For more information, please refer to article below.
OLSB Transition Options:
http://ask.officelive.com/smallbusiness/transition.aspx
If you have backup of your old email, you can create new mailbox at office365, then import your backup to your new mailbox via desktop outlook.
For more information:
You can import your pst(backup):
http://office.microsoft.com/client/helppreview14.aspx?AssetId=HA102505743&lcid=1033&NS=OUTLOOK&Version=14&tl=2

Thanks,
Robert Li

Robert,

Did you look at those instructions?

http://office.microsoft.com/client/helppreview14.aspx?AssetId=HA102505743&lcid=1033&NS=OUTLOOK&Version=14&tl=2

Those are NOT for:  "... you can create new mailbox at office365, then import your backup to your new mailbox via desktop outlook." 

You can tell on the first step that they are not for Outlook (OWA).

Be careful, there is plenty of confusing instructions already.