Is it possible for an item to be moved to another list with its current state?
For example, I have an item with a running Workflow. When I move it, will it still have the same state?
You may apply a workaround for the above requirement. Create a column in the source list named 'Is Moved' and type 'Yes/No' and set the default value as 'No'. Run a workflow to copy the list item from Source list to destination list. Once the item is copied, update the field 'Is Moved' to 'Yes' for that item using the same workflow. You may modify the view of the list to display the list items for which 'Is Moved' field value is not equals to 'Yes'.