How to add attachment without uploading?

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You need the local path to add an attachment:

// add the file to the media library
$attachment = array(
    'post_mime_type' => 'image/png' // the MIME type
,   'post_title'     => 'Attachment title'
);

// Adds the file to the media library and generates the thumbnails.
$attach_id = wp_insert_attachment( $attachment, $path ); // PATH!