Simple Theme Update Example

<?php

function simple_theme_updater( $update_themes, $transient_name ) {

	// We can use the active theme name, because if this code is running, we know this is the active theme.
	$active_theme_slug = get_template();

	$theme = json_decode(
		json_encode(
			array(
				'new_version' => 890,
				'url' => 'https://myfaketheme.com',
				'package' => 'https://myfaketheme.com/my-fake-theme.zip',
			)
		), true, 3
	);

  $theme['theme'] = $active_theme_slug;

	$update_themes->response[$active_theme_slug] = $theme;

	return $update_themes;

}
add_filter( 'pre_set_site_transient_update_themes', 'simple_theme_updater', 10, 2 );