Backup with libimobiledevice
If you have correctly installed libimobiledevice you can easily generate an iTunes backup using the
idevicebackup2 tool included in the suite. First, you might want to ensure that backup encryption is enabled (note: encrypted backup contain more data than unencrypted backups):
idevicebackup2 -i backup encryption on
Note that if a backup password was previously set on this device, you might need to use the same or change it. You can try changing password using
idevicebackup2 -i backup changepw, or by turning off encryption (
idevicebackup2 -i backup encryption off) and turning it back on again.
If you are not able to recover or change the password, you should try to disable encryption and obtain an unencrypted backup.
If all else fails, as a last resort you can try resetting the password by resetting all the settings through the iPhone's Settings app, via
Settings » General » Reset » Reset All Settings. Note that resetting the settings through the iPhone's Settings app will wipe some of the files that contain useful forensic traces, so try the options explained above first.
Once ready, you can proceed performing the backup:
idevicebackup2 backup --full /path/to/backup/