wordpress default provides the functionality when you login from frontends then it will login from backends too. so there is no need any extra plugins or code. just you need to display the wordpress login form in front-ends and which is really very simple. please add below code in your wordpress login-template to login frontend and backend(i mean auto login as you want).
<?php $args = array(
'echo' => true,
'redirect' => ( is_ssl() ? 'https://' : 'http://' ) . $_SERVER['HTTP_HOST'] . $_SERVER['REQUEST_URI'],
'form_id' => 'loginform',
'label_username' => __( 'Username' ),
'label_password' => __( 'Password' ),
'label_remember' => __( 'Remember Me' ),
'label_log_in' => __( 'Log In' ),
'id_username' => 'user_login',
'id_password' => 'user_pass',
'id_remember' => 'rememberme',
'id_submit' => 'wp-submit',
'remember' => true,
'value_username' => '',
'value_remember' => false
);
wp_login_form( $args ); ?>