Hey there,
You need to set full permissions on the exchange. Log in to your Active Directory server and open up the "Active Directory Users and Computers" (under administrative tools).
Once open, navigate to the folder where the users are located. On the top menu click View and select Advanced view.
Right click on the user who's mailbox you want to share, click on Exchange Advanced Tab and select Mailbox Rights. Here add the person you want to give rights to and grant all rights except "Associated External Account".
If you want the user to be able to send email on behalf of the other person, under the Exchange General Tab, select Delivery Options and add the user you want to grant send on behalf permission to.
Under the Security Tab, add this person in with full rights. This should solve your issue.
To add the mailbox in Outlook, the best is to add it in as an associated mailbox. To dothis, click Tools, Email Accounts, select View or Change, click Next, select the exchange account and hit change.
Under More Settings, Advanced Tab add the other user's mailbox by clicking Add then selecting the user from Active Directory. Now click OK until you are out, and restart outlook. You will see that you will have all folders.