Download and set image as Featured Image in WordPress.

functions.php

<?php

// Download and attach image to post.
media_sideload_image($item->image, $post_id, $item->image_caption);

// Then find the last image added to the post attachments.
$attachment = array_values(get_attached_media( 'image', $post_id ))[0];

// Finally set image as the post thumbnail.
if ($attachment) {
    set_post_thumbnail($post_id, $attachment->ID);
}