Older versions of OWA don't provide a way to open other user's folders directly from the interface, as you can from Outlook’s File, Open, Other users folder menu, but this doesn't mean it’s not possible. You need to use a specially formatted URL that contains the other users email address and the folder you wish to open.
You can use the following URL format to open folders you have permissions on. This URL format works in all current versions of OWA, including Office 365 Exchange Online.
This opens the folder without the navigation pane and can be used to open any default folder you have permission to open, provided you know the user's address.
OWA 2007, 2010, 2013 have a dialog box for opening other user's folders, you can use when you are already working in OWA. Click on your name on the upper right side of the screen to access it.
Open the mailbox
When you have permission to the entire mailbox, you can use just the OWA URL and mailbox address, formatted like this:
This opens the other user's mailbox with the navigation pane. Using this URL requires permission to access the entire mailbox; if you don't have the correct permissions this URL will fail with a permissions error.
You can use the following URL format to open folders you have permissions on, replacing folder_name with the name of the folder you want to open.
This URL format will open Calendar, Contacts, Inbox, and Tasks
If you have full permission to the mailbox, you can remove cmd=contents& from the URL.
Opening other folders is trickier, unless you have full access to the mailbox and can use the folder list to select it.
Exchange 2007 and 2010
While you can use these URLs to open another users folder in OWA 2007/2010, there is a dialog box you can use. Click on your name on the upper right side of the screen to access it.
If you don't know the users email address the dialog is easier as it will resolve the name to a mailbox - type the users name into the Select mailbox field and OWA will resolve it. Once you open the folder, bookmark it for later use.