If you find you are having issues with email delivery between O365 (Exchange Online) and On-premises it is possible that the domain is set to outboundonly true
Hopefully the following will resolve your issue
$Cred = Get-Credential
When Prompted enter the following:
User: <enter>
Password: <enter>
$Session = New-PSSession –ConfigurationName Microsoft.Exchange –ConnectionUri https://ps.outlook.com/powershell/ -Credential $Cred –Authentication Basic –AllowRedirection
Import-PSSession $Session –allowclobber
Set-AcceptedDomain -Identity domain.com -OutboundOnly $false