I wrote a simple SMS To Email Forwarder App for android.
I’ve tired to post it on Google play , but they have strict policy when it comes to accessing SMS Messages and they require default handler, which is not the case with this application.
Furthermore , I have uploaded the source code on GitHub for public; If you would have a look you will see the application only listens for incoming new SMS messages (if permission is granted by the user). Once the new SMS has received it will send a copy of it to the Email addressed by the user. (User needs to provided SMTP server information)
This application is handy if you need to access your SMS messages while away from your phone. You might need to disable Battery optimization, to prevent Android to kill the app if it runs in the background and its inactive for a while since the app is not running in a service mode.
Here is the link to APK executable file and you can install it on your phone.
Hope you enjoy it and good luck
– Saeed 🙂