how to update the UI from another thread / parallel task

Use MYCLASS.Dispatcher.Invoke and post code for the queue of the UI thread.
Imagine, you will fill a listbox in an async & await initialized parallel thread or in another object.

...
MyMainWindowInstance.Dispatcher.Invoke(DispatcherPriority.Normal, (Action)  delegate() { MyMainWindowInstance.MyListBox.Items.Add("from parallel!!!!!!!!"); }  );
...

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