Public Folders can only be mail-enabled through the Exchange Management Shell. This means that only email servers with remote administration enabled can be automatically mail-enabled during Public Folder migration.
For Exchange On-Premises as a Destination, remote administration has to be configured in order to allow for this.
For Office 365 Exchange Online, remote administration is always on, so Public Folders are always mail-enabled when migrating to Office 365. If you are not using a Global Administrator account to perform your migration, you will need to make sure that the account being used is a member of either the Organization Management or Recipient Management role group. More information on these role types can be found in the following TechNet article: Sharing and collaboration permissions.
Be sure to update your email address policy on the Destination so that email will be delivered to the correct Public Folder. If you do not change your email address policy, the email address for the Public Folders will be created with the .onmicrosoft.com email address by default.