Grant Read-Only Mailbox Access

Shared Mailbox Access
           Add-MailboxPermission -Identity "[email protected]" -User "ReadOnlyGroup" -AccessRights ReadPermission -InheritanceType all
Shared Mailbox Top Of Information Store
          Add-MailboxFolderPermission -Identity “[email protected]” -User "ReadOnlyGroup" -AccessRights Reviewer
Shared Mailbox Folders
           Add-MailboxFolderPermission -Identity “[email protected]:\Inbox” -User "ReadOnlyGroup" -AccessRights Reviewer
           Add-MailboxFolderPermission -Identity "[email protected]:\Sent Items" -User "ReadOnlyGroup" -AccessRights Reviewer
           Add-MailboxFolderPermission -Identity "[email protected]:\Deleted Items" -User "ReadOnlyGroup" -AccessRights Reviewer
           Add-MailboxFolderPermission -Identity “[email protected]:\Drafts” -User "ReadOnlyGroup" -AccessRights Reviewer
           Add-MailboxFolderPermission -Identity “[email protected]:\Outbox” -User "ReadOnlyGroup" -AccessRights Reviewer

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Setup Read Only Mailbox in Exchange 2003/2007: http://exchangeshare.wordpress.com/2009/07/07/how-to-setup-read-only-mailbox-in-exchange-20032007/

Field Notes of a Computer Geek: Exchange 2010 Mailbox Permissions: http://byronwright.blogspot.com/2011/09/exchange-2010-mailbox-permissions.html

How to Grant Read Access Permission on a Mailbox in Exchange Server 2010/2013: http://messagingserversupport.com/2013/03/03/how-to-grant-read-access-permission-on-a-mailbox-in-exchange-server-20102013/

Microsoft Office 365 Community: http://community.office365.com/en-us/forums/158/t/83744.aspx