Is it possible to move a task from one action list to another?

Yes, it is possible. You can move either a single task or a task including sub-tasks in one step.

1. Click on the Task that you want to move (either click on the name of your task or three dots next to your task to Edit Action) 
2. Go to the Action Location section on the right
3. Choose the Action list, where you would like to move the task, and the relevant main task if applicable
4. Save
5. Go to your new Action list and check the result – your task is moved including its subtask(s)

Note: If you need to see one action in multiple documents, follow this link how-to-show-one-action-in-multiple-documents-related-actions