In Office 365 the Default permission has been given to all Users.
So you need to remove it.

5 Steps total

Step 1: Connect your PowerShell to Exchange Online

$UserCredential = Get-Credential

$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri -Credential $UserCredential -Authentication Basic -AllowRedirection

Import-PSSession $Session -DisableNameChecking

Step 2: Remove rights for group ALL

Remove-PublicFolderClientPermission -Identity “\PF” -User Default

Step 3: Give rights “Editor permission for the users to read and write”

Add-PublicFolderClientPermission “\PF” -User Default -AccessRights Editor

Step 4: Confirm rights for public folder

Get-PublicFolderClientPermission -Identity “\PF”

Step 5: Disconnect from Exchange PS online

Remove-PSSession $Session