Ultimately, there are several ways to accomplish a 'sync' across multiple sites.
However, without more technical information the options are generic at best. Webforms that include uploads or images may require additional work to configure.
Bottom line, the webform data lives in a table in the database, on each site. The best solution may not be a module but rather a cron job pulling that data and serializing it on a collection site. This would be a custom script collating and creating webform content on the collection site. As such, the webform Node ID would not necessarily be preserved.
Another approach, if the cron job is not preferred... might be to use the built-in mail function from webform, or to create a Rule to send the webform data to a mailbox. The collection site can be configured to create node content processed from that mailbox. One benefit is that this could be a non-webform content type. As such, you can add fields and act on that data in a way to manage it and you could also in this way preserve a record of the original Node ID so that a reference to the source site is possible. Other fields might be the site URL, notes, if action is required... and so forth.
Here are some references that might be useful in the latter approach:
- Add content to your site via email using https://www.drupal.org/project/mailhandler - Mailhandler
- http://drupal.stackexchange.com/questions/69134/send-mail-to-email-addresses-from-webform-when-a-content-is-saved - Send mail to email addresses from webform ...
- https://www.drupal.org/project/webform_rules - Webform Rules module
Of course, it matters if you're using D6 or D7. Mailsave & Mailhandler are both included in one popular approach using D6
doesn't have a D7 version.