I want to send a completed form to a customer for their approval

I would like to send a completed quotation form to our customer for their approval.

How do I set this up to send a partially completed form to our customer?

Then how would they approve and send back a fully completed form back to us?

Is Jotform able to allow this kind of setup?

You can pre-populate your form and send a link of pre-populated form to your customer. 

You can pre-populate a form with our pre-populate app:

http://prepopulate.jotform.io/ 

When they submit the form you will receive the Email Notification and you will be able to view the submitted data on the submission page of your form. 

You can also create an approval form. Inside of this guide you can find how to do it:

A General Approach on Building an Approval Process Workflow

Hope this meet what you are looking for.