SMS Backup + 1.5.11 build 1576 Apk is A app to backup sms in android
Download last Version SMS Backup + Apk Donate for Android with direct link
Automatically backup SMS, MMS and call log entries using a separate label in Gmail / Google Calendar. It is also possible to restore SMS and call log entries back to the phone (MMS not supported yet).
Remember to enable IMAP in Gmail.
Please note that auto backup might not work reliably when SMS Backup+ is installed on the SD card. Future version will hopefully fix this, in the meantime please move it back to phone memory if possible.
For those of you worried about app permissions: there is a detailed explanation in the FAQ section of the website.
Also, please consult the FAQ on the website before sending me an email.