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Sorry but there’s not simple answer 🙁
wp_login_form() uses a few filters like login_form_top, login_form_middle etc. to print extra fields but Advanced Google reCAPTCHA uses the login_form action instead to print fields which wp_login_form() function doesn’t call 🙁
You might as well just do it from scratch then trying to modify the plugin to get wp_login_form() working. I will add to our ToDo to maybe add support for it but that’s not simple either as we don’t know in what context it will be used and could end up causing other issues.