I achieved this with getparams in the redirection URL.
In form actions:
Redirect to yoururl.com/?ct-contact-email=#field(234)
You can add multiple params with the corresponding field.
on your thank you page:
Create another form where you could use fields with #query_var (for this example => #query_var(“ct-contact-email”) in a field default value).
Or just read the params manually in your new site.