
Zendesk is a customer service software company that provides a cloud-based customer support platform. This platform enables businesses to manage customer interactions across phone, chat, email, social media, and any other channel you can imagine, all in one place.
Open the form you want to Integrate with Zendesk. Then, enter your Zendesk subdomain.

More details on how to find your subdomain here.
Match the fields in your Fillout form to the corresponding fields in Intercom for the new message. Make sure to include the contact's email, name, subject, and the ticket description.

Once everything is set, click Finish setup on the upper right corner. New form submissions will now create tickets directly in your Zendesk!
Remember to click Publish after making any further changes to the integration.
You can run your integration only when a specific condition is met. Check out this guide.