UPDATE: I installed SENDMAIL and managed it to work.
Using the Moodle eMail Test plugin, the results are:
Logging is not available when using PHP mail() function. However, may find logs on your server. Most common locations on Linux include:
Alernatively, a custom location may be specified using the mail.log setting in php.ini.
The Moodle test message was successfully accepted by PHP Mail.
From : email@example.com
To : firstname.lastname@example.org
However, the emails sent by the eMail Test plugin are stuck in the queue (checked using the MAILQ command).