If Outlook is not sending outgoing messages through VPOP3, it can be a bit hard to diagnose, because Outlook is very bad at error handling, and does not tell the user why it it having problems; the outgoing message will just sit in the 'Outbox' in Outlook.
SMTP Authentication
A common cause of problems sending mail using Outlook is that it is not configured to use SMTP authentication. Unlike most email clients, by default, Outlook's Account setup wizard will often not enable SMTP authentication for sending messages, so if VPOP3 is configured to require authentication, then Outlook will be unable to send outgoing messages (and will not tell the user of the problem).
So, check that SMTP authentication is enabled in Outlook. This is set in the More Settings -> Outgoing Server section of the Account settings in Outlook.
In old versions of Outlook the account settings can be found at File -> Account Settings -> Email Accounts -> Change, but in recent versions of Outlook you have to go to Windows Control Panel -> Mail (Microsoft Outlook 2016) (32-bit)
then Email Accounts to access the full account settings. (Going to File -> Accounts within Outlook itself just gives you a much abbreviated list of options, which does not include SMTP authentication)
Further Diagnostics
If the above doesn't help, then you can usually find more information by going to Send/Receive -> Show Progress in Outlook and select the Errors tab after Outlook has tried to send the message.
Alternatively, you can enable logging in Outlook by following this article: https://support.microsoft.com/en-gb/help/2862843/how-to-enable-global-and-advanced-logging-for-microsoft-outlook
If you look in the 'SMTP log file', then that should show the SMTP transaction between Outlook and VPOP3, so you can see if VPOP3 is reporting any error back to Outlook. In that case, searching for the error returned by VPOP3 will usually let you find the reason for that error message being generated.