To check if the message was sent successfully, you can check the two fields available on SMS History record:

Sent Status
The SentStatus of an SMS gives you the health of the SMS creation process from the salesforce org to the SMS-Magic portal. If it displays “Submitted” in the initial stage, it means that the SMS request has been created successfully.

Delivery Status
The deliveryStatus of an SMS is the real-time delivery report that we receive from the SMS providers. The moment we receive them, we push them back to your SF org.

In short, when we send an SMS from the SF org, a record is created in SMS History tab with the Sent Status as “Submitted”. This means that the SMS has been sent from Salesforce to the SMS Magic portal for further processing. When we receive the delivery report from the provider, we push it back to your org and the Sent Status is updated to “Success” and the Delivery Status is updated with the one shared by the SMS provider.

Additionally, the Status field shows the overall status of the outgoing messages.