How can I save the form after it's emailed to me?

I want to be able to save this form to my documents.

You can enable PDF attachment so that it will also include a PDF copy with the notification. You can easily download that PDF from your notification and serve as a copy of the submitted form.

Guide: https://www.jotform.com/help/503-How-To-Include-Submissions-As-PDF-Attachment-In-The-Email-Notifications

Let us know if you have any questions or if you need further assistance.