To Grant full Access to a Mailbox in Office 365 you must first connect to the remote PowerShell, by typing the 3 commands in your local PowerShell:
$o365cred=get-credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://ps.outlook.com/powershell/ -Credential $o365cred -Authentication Basic -AllowRedirection
Import-PSSession $session
After you are connected, you must run the following command to give Alan full access to Bob’s mailbox:
Add-MailboxPermission -identity Bob@domain.com -user Alan@domain.com -AccessRights FullAccess
If you wanted to give Alan full access to all mailboxes in your environment you would run:
Get-Mailbox | Add-mailboxpermission -user msol.admin@jordansuk.onmicrosoft.com -AccessRights FullAccess