What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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You will basically need to create a supervisor area in your form:
1) In this case you need to create two email notifications one that will go to the supervisor, and the second one that will got o the employee if approved. Please check this guide: http://www.jotform.com/help/25-Setting-Up-Email-Notifications.
2) Make sure to add an edit link in the first notification:
The supervisor will received the notification via email, and will be able to load the filled form via that edit link.
3) You will need to create conditions to send to a specific email address based on a selection, or in this case an answer: http://www.jotform.com/help/167-How-to-send-to-a-specific-email-address-based-on-a-selection
You will basically crate a condition like this:
Here is my demo form: http://form.jotform.co/form/50027934402851
You may clone it to inspect it further: http://www.jotform.com/help/42-How-to-Clone-an-Existing-Form-from-a-URL
Hope this helps, let us know if you have more questions, we will be glad to assist you.