Disclaimer: MySMS has been End of Life without support. You can feel free to use this software, but no support anymore.
Recently the Flash Player relevant issue arises frequently due to the browse policy that the Flash Player has been disabled by default.
MySMS runs properly when Flash Player is enabled on the web page. If Flash Player is not enabled, you probably would meet the issue in the following figure. With prompt: Processing, please wait...
For example, the Chrome browser. Go to the menu: Settings> Advanced> Privacy and security> Content settings> Flash
Add your MySMS address into Allow rules: http://x.x.x.x:8080.
Finally refresh the MySMS page, and test again.