Hi @Kavindu Dayananda ,
According to my research and test, in Exchange 2013, public folders use a mailbox infrastructure to take advantage of the existing high availability and storage technologies of the mailbox database, we could run the following command to check the last time the public folder mailbox was accessed by the user. If there is only one public folder in this public folder mailbox, then this time is the last time the public folder is accessed. We cannot directly get the time when the public folder was last accessed.
Get-Mailbox -PublicFolder <> | Get-MailboxStatistics | fl last*
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