Is it possible and relevan for me to do this process?
User B: Use the old type of phone (ex nokia 103, samsung GT-E1200T)
Is it possible to interact both mobile app and the usage of SMS?
Yes this is possible. I created an app some how similar to that. You will need to have:
1) sqlite database to store your lists. Check this example
2) Send SMS: check this example
3) SMS Broadcast Receiver. check this example: Incomming SMS Broadcast Receiver
check them and let me know if you still need help.