HOW TO ADD MAILBOX PERMISSIONS TO OFFICE 365 FOR 2ND EMAIL
This should be able to be done easily through the web portal but I have found in the past that there are issues with it so here is a workaround in case it doesn't work.
Firstly if you haven't got already install the latest version Powershell.
Then Do a search for Powershell, then right click and "Run as Administrator".
Next, in Powershell, run the command:
$LiveCred = Get-Credential
This will prompt you for your Office 365 admin email and password.
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $LiveCred -Authentication Basic -AllowRedirection
If you get any access denied error messages or anything like that, you probably put your email address and or password in wrong so repeat those steps. At this point it should mention something about importing verbs
If you added permissions already you will need to remove them first so:
Remove-MailboxPermission (SharedMailbox) -User (UserAccount) -AccessRights FullAccess
With (SharedMailbox) as the secondary mail box / email address and (UserAccount) as the primary email address.
The run this command again swapping the SharedMailbox and UserAccount email addresses around.
Add-MailboxPermission (SharedMailbox) -User (UserAccount) -AccessRights FullAccess -AutoMapping $false
Now you should be good to add the mailbox in Outlook by going to File > Account Settings > Exchange > Change (your email address) > Advanced:
In order to also send email as this user, you need to Go into the portal.office.com website > Users > Active Users > Find the user in question > Edit Details > Edit Mailbox Permissions and then add the users who should have permission to send to the various options.
Sometimes the Offline Address Book does not update properly and you need to update it to allow sending by going to Outlook and then:
Send/Receive -> Send/Receive Groups -> Download Address Book...
Should be good.