The SMS Zimlet doesn't do this today (but anyone is welcome to tinker with the SMS Zimlet to make it do so....)
But you can achieve what you're asking for, if your SMS/phone address also has an email address associated with it. If so, you can enter this at the Options/Mail page where it asks "Address for new mail notifications"
For example for my mobile carrier, the email address for my phone is <myphonenumber>@vtext.com For another carrier here in the U.S., the standard is <myphonenumber>@messaging.sprintpcs.com |