If you use the save_post hook, every time content is published or updated, the featured image will be refreshed. Note: make sure ACF is set to return an image ID, which is not its default.
add_action( 'save_post', 'wpse_set_featured_image' );
function wpse_set_featured_image($post_id) {
// get author id
$author_id = get_the_author_id($post_id);
// get author's image
$author_image_id = get_user_meta($author_id, 'your_acf_img_var_name', true);
// fallback image
if(empty($author_image_id)) {
// set to an existing image ID to use as a fallback
$author_image_id = '4';
}
// at last, set the post featured image
set_post_thumbnail($post_id, $author_image_id);
}