Is it possible to open my app through inbox SMS?

You can open your app from a link contained in the SMS.

Create an intent-filter for your domain like this :

<activity
    android:name="ActivityFromSMS" >
    <intent-filter>
        <action android:name="android.intent.action.VIEW" />
        <category android:name="android.intent.category.DEFAULT" />
        <data
            android:host="mydomain.com"
            android:scheme="http" />
    </intent-filter>
</activity>

Then, clicking on a link to http://mydomain.com/... (that can be in an SMS) will prompt the user to open it with your app.

generally you can listen for incomming sms and then just look for number, it came from or it's content, then you can start your desired activity using intent.

Code should look like here. You will need to change the onReceive method