In order to test Office 365 SMTP relay you will have to create a user with an Exchange online license. After the email is activated for this user you can test this user for relay with the following powershell.

First connect to Microsoft Online service with this user that you’ll be using for relaying.

$msolcred = Get-Credential

Next edit the following powershell with the user’s e-mail and the recipient’s too

Send-MailMessage –From RelaySMTPuser@domain.com –To destinationuser@gmail.com –Subject “Test Email” –Body “Test SMTP Relay Service” -SmtpServersmtp.office365.com -Credential $msolcred -UseSsl -Port 587

https://technet.microsoft.com/en-us/library/dn554323(v=exchg.150).aspx

This test is known as Client SMTP submission you can also use a different method for multiple devices where you can configure them all to point to a single server (IIS) in a method known as IIS for relay with Office 365 however, all the methods what involve office 365 (Only) for relay will require a user with Exchange online license assigned to it.

https://technet.microsoft.com/en-us/library/dn592151{308b10a016e19a1cd6a208cbc3961927e16fc6766a4020d3c4ef54ea17925f0f}28v=exchg.150{308b10a016e19a1cd6a208cbc3961927e16fc6766a4020d3c4ef54ea17925f0f}29.aspx

Hope this helps