Almost all of the end user devices are behind the ISP, and many of them are behind many devices in the network hierarchy; Thus, it is extremely rare that the end user device has a public IP address.
Even if you want to start a public server for listening to requests, you do not need to publish the IP address of your device, and a redirect is created on the router that redirects certain requests to your device.
Having said that, you cannot communicate between two end devices using the Internet without a common server between them.
Thus, your possible solution could be : (If you do not want to use an intermediate server), you can send data using mms directly to a mobile phone number.
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