WebViews automatically persist cookies into a android.webkit.CookieManager. Need to store cookies from a WebView into a java.net.CookieManager? Here's one way to do so.

fragment.java

webView.setWebViewClient(new WebViewClient() {
  @Override
  public boolean shouldOverrideUrlLoading(WebView view, String url) {
    String cookieStr = CookieManager.getInstance().getCookie(url); // android.webkit.CookieManager

    storeCookies(url, cookieStr);
    return super.shouldOverrideUrlLoading(view, url);
  }

  // Convert cookie string into a list of cookies.  Persist cookies in a java.net.CookieStore
  private void storeCookies(String url, String cookieStr) {
    if (cookieStr != null && !cookieStr.isEmpty()) {
      URI uri = new URI(url);
      List<HttpCookie> cookies = HttpCookie.parse(cookieStr);
        for (HttpCookie cookie : cookies) {
            cookieStore.add(uri, cookie); // java.net.CookieStore from a java.net.CookieManager
        }
    }
  }
}