SMS on MY PC

The tmomail.net function is a really low capability service, and it has become a target for many scammers over the years. Due to that, there are a lot of filters in place to try and prevent bad activity and protect our customers. Normally, if your message is caught in that filter, you will get some kind of notification on the sending email that the message was blocked or failed to send for some reason. Since you are not getting any kind of error or notification, I would be curious to try it to a phone number that is not on your account. Have you tried to send to someone else on T-Mobile that is not connected to your own account?