Hi BWJS,
To understrand the issue better, I’d like to confirm the following information:
1. When you say “we able to access two public calendars using a link (via their smartphones)”, do you mean this calendar is shared by other users?
2. How is the calendar moved to Office 365 Exchange Online?
3. How are the public folders moved to Office 365 Online? Have you used the following article to move the public folder?
http://technet.microsoft.com/en-US/library/jj983799%28v=exchg.150%29.aspx
If yes, generally speaking, the public folder permissions exist after the migration.
If not, please give me more detailed steps about how you moved the public folders to Office 365 Exchange Online, then I can do further troubleshooting.
Thanks,
Vivian Wang