You can move a task to another project in the source service and Pleexy will keep the task synced as long as the project it was moved to is selected in your connection's Source Settings. The task will stay in the same project in the destination.
If you move tasks to another project in Todoist, Pleexy will still keep your tasks synced between Todoist and the source service. However, the task will remain in its original project in the source.
If you move a task to another list in Microsoft To Do, the task will be completed in the source due to To Do API restrictions.