Sendmail doesn't send email to same domain
I'm using a thirdy part provider for email boxes and domain registration.
From this provider I've redirected my domain to a DO VPS running Ubuntu 14.04.
Using SENDMAIL if I send an email to firstname.lastname@example.org (or @otherdomain.ext) all works great, but if I send an email to xyzqwe@SameVPSDomain.ext it doesn't work.
What is the problem?
Why from DO droplet I cannot send email to a thirdy part email provider??
Thanks in advance.