Forward iMessages and SMS to e-mail? I want to forward all SMS and iMessages received on my iPhone to my e-mail address. I have tried IFTTT, but can't see a way to do it. Has anyone else managed to do this?
you need to have your email address turned on for iMessage on your
  iPhone in order to enable Text Message Forwarding. If you don’t, the
  numeric access code will not appear on your iPad or Mac during the
  setup process. As soon as you enable your email address for iMessage
  (you only need to do this on your iPhone) the numeric access codes
  appear as expected. Once you have text message forwarding setup you
  can disable your email address again in iMessage as it seems to only
  be necessary for the numeric access code setup step, not the actual
  text message forwarding itself.`
  
  To enable your email in Messages, grab your iPhone and head to
  Settings > Messages > Send &amp; Receive. There, you’ll find all of the
  addresses at which you can be reached via iMessage. Enable your iCloud
  email address by tapping on it, then head back to your Mac or iPad and
  again request the pairing verification code from the Messages app.
  This time, you should see a box appear on your iPhone in which you can
  enter the code.


Source: http://www.tekrevue.com/tip/sms-relay-configuration-fix/