Any SharePoint Client, User, or Developer need an SMTP server to send e-mails to Internal or External SharePoint site users from a Workflow, Alerts, Request Site Access, and/or Any custom Apps that use SharePoint Outgoing e-mail setting to send e-mails.
SharePoint cannot be configured to send e-mail over encrypted port to the e-mail service. And Office 365 and Gmail required an SMTP connection that supports TLS encryption .
Fortunately, Windows Server (2008-2012) supports an SMTP relay for Office 365 and Gmail by install a local SMTP Rely Server that supports an encrypted connection (over TCP Port 587) .
The Steps are easy and forward:
Install SMTP Role (Windows Server 2008 and 2012)
Configuring SMTP Service to Relying to Office365/Gmail SMTP
Testing the SMTP Service Connection
Configuring Outgoing E-Mail settings in SharePoint Servers
Test Sending an E-mail from SharePoint Site
The following is the detailed steps: