How can I have multiple people fill in different parts of the form?

Hello,

How can I have person A submit part of the form, and then have person B submit the rest of the form?

I would like to set it up so that after A submits the form, the email notification will be sent to person B where they will be able to edit the form and then once they submit it, have the email be sent to a different email.

The idea is for an employee to fill out a form (person A), then have the supervisor review and provide their e-signature (person B), and have the form be submitted to the HR.

The best way to set this up would be to use conditional emails containing edit submission links.  The following thread has a walk through on how to set up a full approval workflow:

https://www.jotform.com/help/432-A-General-Approach-on-Building-an-Approval-Process-Workflow

Though for your needs, simply sending the edit submission links may be enough:

https://www.jotform.com/help/40-How-to-Let-Users-Update-Their-Form-Submissions-at-a-Later-Date