How can I set up a form letter to automatically send to an external email?

What I am trying to set up is a pre worded form letter that people can add their contact info to and when they click submit the letter and individuals info goes to another organization. 

You can edit the content of the email notification using the Email Editor. You can even inject the answer of the user in the content. Just click the "Form Fields" drop down and choose the field value you want to appear in the email content. It is enclosed by curly braces {}.

You can actually change the email recipient of the form notification. In this way, the notification will be sent to the assigned email address. In the Recipients tab of the notification, you can add, edit or remove a recipient.

Please check these guides:
Setting-Up-Email-Notifications
How-to-Properly-Add-Change-and-Test-a-New-Email-Recipient-Address

Hope that helps. If you have any questions, let us know. Thank you.