Hi Munsu,
There is no documentation about how to migrate public folders from SBS 2003 to Office 365 at this time.
As a workaround, you can open an Office 365 mailbox that has the corresponding permission of the Office 365 public folder and an on-premise mailbox in the same profile via the Outlook desktop client. After that, drag and drop the contents from the on-premise public folders to the Office 365 public folders.
For detailed information about public folders in Office 365, please refer to the following article.
http://technet.microsoft.com/en-us/library/jj966272(v=exchg.150).aspx
Thanks,
Edward Qu