The Save Files app downloads any files from the Internet to your Dropbox or Google Drive. It uses the Filepicker API but this can also be done through Google Apps Script.

This Google Script takes the URL of a file and downloads it to your Google Drive. You need to specify the full URL of the file and also the destination folder on Google Drive where that file would be saved.

function downloadFile(fileURL, folder) {
  var fileName = '';
  var fileSize = 0;

  var response = UrlFetchApp.fetch(fileURL, { muteHttpExceptions: true });
  var rc = response.getResponseCode();

  if (rc == 200) {
    var fileBlob = response.getBlob();
    var folder = DocsList.getFolder(folder);
    if (folder != null) {
      var file = folder.createFile(fileBlob);
      fileName = file.getName();
      fileSize = file.getSize();
    }
  }

  var fileInfo = { rc: rc, fileName: fileName, fileSize: fileSize };
  return fileInfo;
}