Once we configured the SharePoint outbound mail server then our responsible to test the setup. Here the small powershell snippet will do!
### The script will return True or False
$toemail = "firstname.lastname@example.org"
$subject = "Test - SharePoint Outbound mail"
$body = "This mail for testing purpose...! Please ignore your action!"
$site = New-Object Microsoft.SharePoint.SPSite "http://sharepoint/"
$web = $site.OpenWeb()
If you get “True” the configuration perfectly alright, else you have to check the ULS log to find an issue. Suppose if you are not getting a mail you have to check smtp log or address to exchange/wintel team.