If you’re ever want to check that your messages have been sent successfully, you can always run a Message Log Report from your SMS Central account.
Login to your account, click on the Reports tab and then Message Log Report.
Once there, you’ll be able to filter the report based on the categories that you’re interested in, such as messages sent within a particular date range, or messages sent from one of your dedicated numbers, for example.
Click Run when you've applied all your filters and the report will list all your SMS details.
Sent messages will be grouped according to their status (Delivered or Bounced). Clicking on the message will display all the details.
For more info, you can read this support article.