JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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You can still send the existing uploaded submission files in your jotform by re-submitting the form after integrating the form to Dropbox.
You can re-submit the form again in the View Submissions page of the form.
user guide: -How-to-view-Submissions
Click on the EDIT button and then click Submit button.
You will have to do this for each existing submissions if you want the uploaded file to be copied also to the Dropbox account integrated on the form.
Hope this help. Let us know if you need further assistance.