This steps are not authorized by Microsoft and probably even not allowed, but still this is only option to gain access to Exchange Online Shared mailbox from Windows Phone device with push delivery.
(get-item C:\Windows\System32\WindowsPowerShell\v1.0\Modules\MSOnline\Microsoft.Online.Administration.Automation.PSModule.dll).VersionInfo.FileVersion
$msolcred = get-credential connect-msolservice -credential $msolcred
Get-MsolUser -UserPrincipalName "sharedmailbox@account.onmicrosoft.com" | Set-MsolUserPassword
Running this command will reset password to this inbox to temporary password that will be printed to stdout.