The GUI in Office365 and Azure is great but sometimes we need to dig deeper.
I ran into some issues with a Resource mailbox and had to do some troubleshooting.

I always start with turning off Execution Policy, because frankly it usually screws up what I’m trying to do.

Set-ExecutionPolicy Bypass

This will allow you to run all kinds of Powershell-scripts, it’s like turning off UAC for your shell (with caution!).

Then start a regular Powershell in elevated mode and write the following:

$LiveCred = Get-Credential

$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection

Import-PSSession $Session

The console will load the modules and commands necessary, so you won’t have to do it manually.

More information can be found at: http://help.outlook.com/en-us/140/cc952755.aspx