Update Secondary Submission on Form Submission

I'm in the process of setting up an internal application form, and part of the application is requiring the employee's manager's approval. I have it set up so completing the form triggers an email with a link to a secondary approval form to the manager, but I'd like to be able to update a field on the original application form with the manager's approval automatically when it's submitted rather than keeping up with applications and approvals separately. Is there any way to accomplish this?

If I can understand you correctly, you are using two different forms, and you are looking for a way to use only one.

I think this could be possible by using conditions, you may add a text field where your manager should enter a code, something that only he/she will have, you should provide this code and then show a check box or radio button to approve the submissions, take a look on this guide to get detailed info about conditions: http://www.jotform.com/help/57-Smart-Forms-Using-Conditional-Logic. 

This guide may help you as well: http://www.jotform.com/help/316-How-to-show-or-hide-a-field-in-the-form-based-on-the-other-field-input-or-selection.