How to Update the binding from other window in wpf?

Question

I have one observable collection binds to combo box.

Below is the Xaml

<ComboBox Name="Combo" HorizontalAlignment="Left" VerticalAlignment="Top" Width="120" 
    ItemsSource="{Binding Path=coll}"/>
<Button Content="Button" Click="Button_Click_1" HorizontalAlignment="Left" VerticalAlignment="Top" 
    Width="75" RenderTransformOrigin="0.649,3.417" Margin="10,36,0,0"/>

Below is my code

public partial class MainWindow : Window, INotifyPropertyChanged
{

    public event PropertyChangedEventHandler PropertyChanged = delegate { };
    public ObservableCollection<string> _coll { get; set; }
    public ObservableCollection<string> coll
    {
        get
        {
            return _coll;
        }
        set
        {
            _coll = value;
            PropertyChanged(this, new PropertyChangedEventArgs("coll"));
        }
    }

    public MainWindow()
    {

        InitializeComponent();

        coll = new ObservableCollection<string>();
        coll.Add("ABC");
        coll.Add("AAA");
        coll.Add("BBB");
        coll.Add("KKK");
        Combo.SelectedItem = coll[0];

        DataContext = this;
    }

    public MainWindow(string data)
        : this()
    {
        coll.Add(data);
    }

    private void Button_Click_1(object sender, RoutedEventArgs e)
    {
        Window1 window = new Window1();
        window.Show();
    }
}

Now I am opening new window on button click event and I am passing the data from the second window to Mainwindow in this case binding is not working

Second window Xaml

<TextBox Name="txtBox" HorizontalAlignment="Left" Height="23" TextWrapping="Wrap" 
    VerticalAlignment="Top" Width="120"/>
<Button Content="Button" Click="Button_Click_1" HorizontalAlignment="Left" 
    VerticalAlignment="Top" Width="75" Margin="10,28,0,0"/>

Code

public partial class Window1 : Window
{
    public Window1()
    {
        InitializeComponent();
    }

    private void Button_Click_1(object sender, RoutedEventArgs e)
    {
        MainWindow obj = new MainWindow(txtBox.Text);
        this.Close();
    }
}

Answer 1

In your main window you have to add observable collection to other Constructor, Otherwise Observable Collection has no data.

public MainWindow(string data)
    : this()
{
    coll = new ObservableCollection<string>();
    coll.Add("ABC");
    coll.Add("AAA");
    coll.Add("BBB");
    coll.Add("KKK");
    Combo.SelectedItem = coll[0];

    DataContext = this;

    coll.Add(data);  
}

this works if you create another instance of the mainwindow.