The files author-course.php and author.php can not be overwritten in a WPLMS child theme directly. The only way is to override the filter in the child theme functions.php:

add_filter( 'template_include', 'override_check_instructing_courses_endpoint',99);

function override_check_instructing_courses_endpoint($template){
  if(!is_author())
    return $template;
  global $wp_query;
  $instructing_courses=apply_filters('wplms_instructing_courses_endpoint','instructing-courses');
  if ( !isset( $wp_query->query_vars[$instructing_courses] ) ){
     $wp_query->set( 'post_type', array('post') );
     return get_stylesheet_directory().'author.php';
  }else{
  
    $wp_query->set( 'post_type', array('course') );
    return get_stylesheet_directory().'author-course.php';
  }
}

add_filter( 'template_include', 'override_check_instructing_courses_endpoint',99);

function override_check_instructing_courses_endpoint($template){

if(!is_author())

return $template;

global $wp_query;

$instructing_courses=apply_filters('wplms_instructing_courses_endpoint','instructing-courses');

if ( !isset( $wp_query->query_vars[$instructing_courses] ) ){

$wp_query->set( 'post_type', array('post') );

return get_stylesheet_directory().'author.php';

}else{

$wp_query->set( 'post_type', array('course') );

return get_stylesheet_directory().'author-course.php';

}

“WPLMS is a Learning Management System for WordPress. It is an e-learning WordPress theme for course management, instructor and student management using which you can create and sell your courses online. “

Override WPLMS author-course.php / author.php in child theme

Alexander