How can a field remember the last value?

If the user are using the same computer browser and the cache or cookies hasn't been clear yet, then the previous entered value will appear in a suggestion drop down.

I'm not sure if this is what you need but you can actually prepopulate the form field using the URL parameter. Here's a guide: Prepopulating-fields-to-your-JotForm-via-URL-parameters . You can also use this app: http://prepopulate.jotform.io/

If you want to populate value from one form field to another then you need to use the conditions. Please check this guide: How-to-Populate-Field-with-a-Value-from-another-Field

If this is not what you need, let us know. Also, please provide more information about your issue. Thank you.