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Yes, this is possible. There are two options that you can choose from.
Option #1: You can set a session ID and allow them to fill it out using a custom URL that has the session ID on it. Here's a guide on how to do that: https://www.jotform.com/help/97-How-to-Save-Forms-and-Continue-Later
Option #2: You can enable the "Auto Fill" feature, however, compared to option 1, the auto fill feature only saves the current progress on the user's browser, which means he/she can only continue filling out the form on the same computer and same browser. Another problem is that if you have multiple users using the same computer or browser, then only one progress can be saved. Here's a guide for that: https://www.jotform.com/help/227-How-to-Enable-Auto-Fill-Feature.
I personally recommend going for option #1 as it gives your users to freedom to continue their progress regardless of what device they are using, as long as they have the session URL.
Let us know if that works.