Can a recipient of a form fill out part of it, save the form, and come back to it later and then send it to me?

Yes, it is possible to have this kind of function here in JotForm. We do have a feature where your users can save the form and continue it later. Please refer to this helpful guide: https://www.jotform.com/help/97-How-to-Save-Forms-to-Continue-Later.

Hope that helps. If you have any questions, let us know. Thank you.