Android webview: download files like browsers do

Finally i decided to look for the
DownloadHandler from the Android Stock Browser code.
The only noticeable lack in my code was cookie (!!!).

Here’s my final working version (DownloadManager method):

    wv.setDownloadListener(new DownloadListener() {
        @Override
        public void onDownloadStart(String url, String userAgent, String contentDisposition, String mimeType, long contentLength) {
            DownloadManager.Request request = new DownloadManager.Request(Uri.parse(url));

            request.setMimeType(mimeType);
            //------------------------COOKIE!!------------------------
            String cookies = CookieManager.getInstance().getCookie(url);
            request.addRequestHeader("cookie", cookies);
            //------------------------COOKIE!!------------------------
            request.addRequestHeader("User-Agent", userAgent);
            request.setDescription("Downloading file...");
            request.setTitle(URLUtil.guessFileName(url, contentDisposition, mimeType));
            request.allowScanningByMediaScanner();
            request.setNotificationVisibility(DownloadManager.Request.VISIBILITY_VISIBLE_NOTIFY_COMPLETED);
            request.setDestinationInExternalPublicDir(Environment.DIRECTORY_DOWNLOADS, URLUtil.guessFileName(url, contentDisposition, mimeType));
            DownloadManager dm = (DownloadManager) getSystemService(DOWNLOAD_SERVICE);
            dm.enqueue(request);
            Toast.makeText(getApplicationContext(), "Downloading File", Toast.LENGTH_LONG).show();
        }
    });