Many organizations have Public Folders setup for shared access to information across a team or workgroup. Public folder migration will be dangerous without proper preparation and Execution. If you follow manual methods, you need to go through long procedures and complex PowerShell commands. To avoid all these problems, it is worth to follow third party tool like Shoviv Exchange Server Suite. This software migrates multiple public folder mailboxes to Office 365 mailboxes without size limitations.
For more information- Public Folder to Office 365 Migration