Is it possible to transmit short messages similar to mobile phone short messages in RF range?

This question is really difficult to answer. If the frequency used by the radio is transmitted directly to the mobile phone, it will definitely not work. The frequency is inconsistent. Radio frequency uses several frequency bands between 500 kHz and 108 MHz, and mobile phones use 900MHz or 1800MHz.

Just like pagers in the past, you can send radio waves to pagers from paging stations (transmitting stations) to transmit text messages. If these devices are designed for two-way transmission, they can also send short messages to each other like mobile phones. The frequency used in this launch can be arbitrarily designed, and it can also emit radio frequency in the radio frequency range. Just in order not to interfere with radio broadcasting, a much higher radio frequency is generally adopted; In addition, all countries in the world have a unified management organization (Radio Management Committee) to make overall allocation and rational use of radio frequency resources.

So, the answer to your question can be: make it work, but don't make it work.