SMS2Mail

Mail SMS forwards your incoming text messages (SMS) to your E-Mail Inbox. You may use MailSMS for

1. Creating online backup of your messages on the go
2. Viewing the Messages coming to your home phone while you are roaming
3. Getting all messages in your phone, tablet etc in one place - your email inbox

Just install the app, enter your email id, save it and voila you are done setting up MailSMS.
This app requires a live internet connection in your device. If your device goes offline, the app will wait for up-to 8 hrs for the device to come back online to forward your messages.
MailSMS requires two permissions:
Permission to access incoming messages
Permission to access internet
We store your e-mail address on our servers. We value your privacy and will not spam. Your messages are send via our servers, but we do not store your message on our servers.