Cron job to transfer files to remote server
If you absolutely need it, Drupal has hook_cron() for regular task running:

function MYMODULE_cron() {
  // Copy your files here using standard php FTP functions
}


But it would be considerably more efficient to leave Drupal out of this altogether, and set it up with a basic rsync/FTP cron job executed on the server.

Alternatively, Backup and Migrate can both take a dump of the public/private file system and transfer it to an FTP target. Again, a solution outside Drupal will always be more efficient as it won't bootstrap the application.