How can my client log back into the form they started filling out?

You can enable your form's autofill on your form settings. This autofill allows your users to fill up the form, and continue them later by saving the information on their browser. You can check this guide for more information on how to enable this feature: https://www.jotform.com/help/227-How-to-Enable-Auto-Fill-on-Forms

Thanks.