I am prepping to perform the process listed here "Configure legacy on-premises public folders for a hybrid deployment". Step 4 indicates that you should run Sync-MailPublicFolders.ps1 -Credential (Get-Credential) -CsvSummaryFile:sync_summary.csv
If I understand the process correctly, the Office 365 mailboxes are accessing the public folders directly on prem so I am confused at to what exactly is synchronizing when you run the Sync-MaillPublicFoders script?