Custom field not being saved in the Address book

Hi,

I have added a custom billing field to my checkout page called Alternate Phone Number. I use the following code in my functions.php to add it to the checkout page:

/* Additional Phone number field to Checkout page */
add_filter( 'woocommerce_checkout_fields' , 'woocommerce_checkout_field_editor' );
// Our hooked in function - $fields is passed via the filter!
function woocommerce_checkout_field_editor( $fields ) {
    $fields['billing']['billing_field_value'] = array(
        'label'     => __('Alternate Phone Number', 'woocommerce'),
        'placeholder'   => _x('Alternate Phone Number', 'placeholder', 'woocommerce'),
        'required'  => false
    );
    return $fields;
}
/* Display Additional Phone number field in Orders page*/

add_action( 'woocommerce_admin_order_data_after_billing_address', 'edit_woocommerce_checkout_page', 10, 1 );
function edit_woocommerce_checkout_page($order){
    global $post_id;
    $order = new WC_Order( $post_id );
    echo '<p><strong>'.__('Alternate Phone Number').':</strong> ' . get_post_meta($order->get_id(), '_billing_field_value', true ) . '</p>';
}

But the field is not getting saved in the address book.
How can I get the Address book plugin to save this additional field data?

Thanks!