Is it possible to have an option at the end of the survey for the person to send an email of the form to someone else?

Hi Jenni!

It is possible if the respondent includes an email address on the form itself before clicking Submit. An autoresponder is automatically created in the form Settings>Emails to send the submission data to the specified email address. You can add an additional email field for the respondent to enter their own email address, and create an autoresponder email to be sent to them.  It is not possible for the respondent to enter an email address after they click Submit as they can be presented with either a Thank You page, or redirected to a custom URL.

Guide: Setting-up-an-Autoresponder-Email

I have cloned your form and added the two email fields for you to try and see how it works! Here is the form: https://form.jotform.com/91075540255959. Please clone it and and see if this works for you.

Guide: How-to-Clone-an-Existing-Form-from-a-URL

So if I download this pdf and put it on my site, when a client opens the email and fills it out and includes the email address of who they want it sent to, it should automatically send to that person as soon as they click the submit button correct?
I tried this and put in my own email address as a test and never received it.
...

To confirm, is this the form that you tested:

https://www.jotform.com/91075989511163

I ran the same tests as you and submitted that form, used my email address for both email fields (Please enter your email and Please fill out the email address of someone you would like to share the survey results with!), and got two emails after submitting the form:

The two Autoresponders that were configured in that form worked as expected. If you tested a different form though, please share the form URL with us so we can have a closer look on how your Autoresponders were configured.