I made a tutorial on how to make contact form 7 go to a thank you page once a user submits a message. Here it is:
https://www.compse.com/forum/website-design-forum/redirect-to-a-thank-you-page-with-wordpress-contact-form-7/
Once you have done that just put Googles conversion code right into the html side of your WordPress thank you page.
I hope this helps.
Shawn
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