It can be build using Integromat, a no-code workflow automation tool. Integromat allows you to create automated scripts using a simple drag-and-drop interface for non-technical users. This is a ready-made scenario, but it can be customized by adding more apps, actions, filters or branches.
Categories
Teamwork can also be integrated using automation tools other than integromat:

When this trigger fires in Teamwork
Triggers when a new task is added.
Then these actions happen in Teamwork
Adds a new task to a specified task list.
Deletes a task with a given ID.
This guide contains information on how to set up an automatic workflow that allows to Move completed tasks between Teamwork projects.
Part I
First, we need to connect Teamwork to Make.com.

Create Make.com account.
Create Make.com account if you don't have one.

Connect Teamwork to Make.com.
Give Make.com access to your Teamwork account, using Teamwork credentials.
Part II
Next, we need to create a workflow automation scenario using graphical no-code web interface of Make.com.

Set up a Trigger action for Teamwork
Choose the following trigger: Watch tasks (Triggers when a new task is added.).

Then set up an Action for Teamwork
Choose this action: Create a task (Adds a new task to a specified task list.).

Then set up another Action for Teamwork
Choose this action: Delete a task (Deletes a task with a given ID.).
Part III
Finally, we need to test this automation and publish it.

Customize data flow
Configure the data that is exchanged between Teamwork.

Test the workflow and turn it on for production use
Test your scenario and publish to production. Now you have an automatic workflow, that will Move completed tasks between Teamwork projects!
Triggered when you add a new task.
New task (instant)
New task deleted (instant)
New task updated (instant)
Triggered when you add a new project.
Triggers when a new task is added.
Creates a new task.
Updates an existing task.
Delete task
List project tasks
Creates a new project.
Uploads a file to a project.
Make.com (Integromat) is a powerful automation tool that enables users to connect their favorite apps, services, and devices without any coding skills. With its unique features, users can automate even complex integrations easily and efficiently, saving time and effort. Integromat allows to connect apps and automate processes in a few clicks.