How to configure an SMTP relay for Office 365. We no longer have an on-premises messaging environment.

You can walk through the options here:

https://technet.microsoft.com/en-us/library/Dn554323(v=EXCHG.150).aspx

How to set up a multifunction device or application to send email using Office 365

Build SMTP ISS role (could be under WNLB as well for HA), make a changes in DNS to authorize your public IP's to send as your domain.

Hi,

According to your requirement, you need to install an IIS SMTP relay server in your internal network, configure it to accept, and forward emails to Office 365.

Please refer to these below links

https://technet.microsoft.com/en-us/library/dn592151(v=exchg.150).aspx

http://blogs.technet.com/b/hot/archive/2012/04/26/how-to-configure-iis-smtp-cloud-relay.aspx

In addiction,  as this forum focuses on some general discussion about Exchange, if you have other requirements about office 365, I suggest we can ask a question in office 365 forum for more help:

https://community.office365.com/en-us/f/

Thank you for your understanding.

Regards,

David