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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Yes, your users can save the form submission by different ways. Here are the things that you can try:
In the "Compose Email" window, you can add the fields that you want to show to show to the user who will be receiving the email. You can also add the PDF link tag so that they can download a PDF copy of it.
2. You can also enable the "Print" option in your submit button so that they can print it directly before submitting the form.
Here's a guide on how to do that: http://www.jotform.com/help/24-Print-Button-on-Forms
Let us know if you need more help on this.