Access To another mailbox

If you are talking about the access to the user who left company to other user.

open the user properties in Exchange Server Console(EMC)
1.In the console tree, navigate to Recipient Configuration > Mailbox.
2.In the result pane, select the mailbox for which you want to grant Full Access permission.
3.In the action pane, under the mailbox name, click Manage Full Access Permission. The Manage Full Access 4.Permission wizard opens.
5.On the Manage Full Access Permission page, click Add.
6.In Select User or Group, select the user to which you want to grant Full Access permission, and then click OK.
7.Click Manage.
8.On the Completion page, the Summary states whether Full Access permission was successfully granted. The 9.summary also displays the Shell command used to grant Full Access permission.
10.Click Finish.

then you can add this mailbox as a additional mailbox in outlook.

If you only want to give the access to the mails of left user, i would suggest to export the PST and attach it to the user outlook.

Hi,

You need to add permissions for the user to access the old employees mailbox. You can do this a few ways.

Try this from the EMS

Add-MailboxPermission "Old Employee Mailbox" -User "User who needs mailbox access" -AccessRights FullAccess

Once the user has Full access they can open via File > Open > Other USers Folder

How to Allow Mailbox Access
http://technet.microsoft.com/en-us/library/aa996343(EXCHG.80).aspx