migration.php

<?php

/**
 * Comments Migration
 *
 */
function ea_comments_migration() {

	$site_url = 'https://yoursite.com';
	$username = 'your_username';
	$password = 'your_password';

	$query_args = array(
		'per_page' => 20,
		'context' => 'edit',
	);

	$request_args = array(
		'headers' => array(
			'Authorization' => 'Basic ' . base64_encode( $username . ':' . $password ),
		),
	);

	$url = add_query_arg( $query_args, trailingslashit( $site_url ) . 'wp-json/wp/v2/comments' );
	$response = wp_remote_get( $url, $request_args );

	if( '200' != wp_remote_retrieve_response_code( $response ) )
		return;

	$comments = json_decode( wp_remote_retrieve_body( $response ) );
	if( empty( $comments ) )
		return;

	// Reverse them so we start with oldest first
	$comments = array_reverse( $comments );

	// Save Old/New IDs for parent linking
	$comment_ids = array();

	foreach( $comments as $comment ) {

		// Skip if comment exists
		$existing = get_comment( $comment->id );
		if( !empty( $existing ) && ! is_wp_error( $existing ) )
			continue;

		$parent = !empty( $comment->parent ) && array_key_exists( $comment->parent, $comment_ids ) ? $comment_ids[ $comment->parent ] : $comment->parent;

		$commentdata = array(
			'comment_post_ID' => $comment->post,
			'comment_author' => $comment->author_name,
			'comment_author_email' => $comment->author_email,
			'comment_author_url' => $comment->author_url,
			'comment_content' => $comment->content->raw,
			'comment_type' => '',
			'comment_parent' => $parent,
			'user_id' => $comment->author
		);

		$id = wp_new_comment( $commentdata, true );

		if( ! is_wp_error( $id ) )
			$comment_ids[ $comment->id ] = $id;
	}
}
//add_action( 'init', 'ea_comments_migration' );