How would you like to get your new text messages? On your phone? Your Desktop? Or on your Email/Gmail account? You can easily use the IFTTT service to automatically forward text messages to Email on Android phone, by doing as follows:
1. Download and install IFTTT Android app from Google Play Store (Download Link)
2. Sign-in (sign-up) to the service
3. Tap the "My Recipes" button on the top right
4. Tap the Add button to start creating a new Recipe, and then tap the Start Now button
5. Use the Search box or scroll over available Triggers, and select the Android SMS option
6. Under the Android SMS options, tap the "Any new SMS Received", so the trigger get activated when a new text message arrvies
7. Now it's time to select the Action. Find Gmail, and tap the "Send an email" option.
8. Now you just need to enter your Email address, so as soon as receiving a new text message, the IFTTT service automatically forward that specific SMS to your email address via your Gmail account.
Note that, you may need to grant the IFTTT to have access to your Gmail account to view and manage your mail and view your email address.
If you are confused, the following illustrated tutorial will definitely come handy: