Opposed to many articles on this topic, IT IS possible to create and use a shared mailbox in your normal mail client.
Just like you would your office365 account.

Yes, you can use Outlook, the OWA app or OWA in the browser, but like myself I rather have it like a normal mailbox in Outlook 2013 / Windows Mail / Windows Phone 8 / Mac Apple mail / iPhone / iPad or even Android.
To get this working, here's a brief summary:

• Create an Office365 shared mailbox
• Reset the password
• Update the password in Outlook Web Access
• Setup the shared mail account in your favorite mail client

Previously this method wasn't possible, but due to some changes, I believe related to the implementation of Azure AD into Office365, we have this solution available.