Head over to the Play Store and install Super Backup, or open this link on your device and hit install
Open the app and head into Call Logs
Specify where you’d like to save the backup file and hit OK
You’ll be prompted by a Successful message and it’ll ask you whether you’d like to upload the file somewhere
That’s it, you’ve successfully backed up your Call Logs
Note: Make sure you copy the backup file to a safe location on your computer. You’ll need to connect your phone to your computer and navigate to the folder which you specified above. If you’ve uploaded the file somewhere you won’t need to do this.