With a design based in Material and inspired in the contact app included in Lollipop, this app allows you to make backups from the calls log and from the database of messages. You can then delete the calls and messages, reloaded into the system log, etc.
In contrast, due to the limitations of Android, the backup of outgoing messages is held every few hours, in a background process.
Furthermore, the app will show the call log or messages with a comfortable and intuitive interface and can answer calls or messages received from the application itself.
As for calls and received messages, if you activate the option, the backup will be performed as soon as the corresponding event occurs.
Telephony Backup v1.13.78 Apk