Question

I have a view model with some fields, i.e.

type ViewModel =
    member x.a = [1;2;3]
    member x.b = [4;5;6]
    member x.c = [7]

and in WPF application places some views, as:

<Control.Resources>
                    <DataTemplate x:Key="ItemTempl">
                        <TextBlock Text="{Binding}" />
                    </DataTemplate>

                    <DataTemplate x:Key="SomeTempl">
                        <ListBox ItemsSource="{Binding}"
                                 ItemTemplate="{StaticResource ItemTempl}" />
                    </DataTemplate>
                </Control.Resources>

                <StackPanel>
                    <TabControl x:Name="ListBoxViewPresenter">
                        <TabItem Header="vm.a" Content="{Binding vm.a}" 
                             ContentTemplate="{StaticResource SomeTempl}"/>
                        <TabItem Header="vm.b" Content="{Binding vm.b}" 
                             ContentTemplate="{StaticResource SomeTempl}"/>
                        <TabItem Header="vm.c" Content="{Binding vm.c}" 
                             ContentTemplate="{StaticResource SomeTempl}"/>
                    </TabControl>
                    <ListBox x:Name="ListBoxViewPresenter">
                        <ListBoxItem Content="{Binding vm.a}" 
                                     ContentTemplate="{StaticResource SomeTempl}" />
                        <ListBoxItem Content="{Binding vm.b}" 
                                     ContentTemplate="{StaticResource SomeTempl}" />
                        <ListBoxItem Content="{Binding vm.c}" 
                                     ContentTemplate="{StaticResource SomeTempl}" />
                    </ListBox>
                </StackPanel>

What should I do to achieve such behavior:
when you clicked on some element in vm.a/b/c in ListBoxViewPresenter so same element in ListBoxViewPresenter is must selected in corresponding TabItem.

UPD:
Specifically my real problem, changing from origin topic.

I have ViewModel with fields: onelines, twolines… and a field with name selected_scheme.
In xaml:

<TreeViewItem Header="{Binding Path=name}" x:Name="ProjectArea">
                    <TreeViewItem Header="Однониточные планы" Style="{StaticResource MyTreeViewItem}">
                        <ContentPresenter Content="{Binding onelines}" ContentTemplate="{StaticResource SchemeWrapperTemplate}" />
                    </TreeViewItem>
                    <TreeViewItem Header="Двухниточные планы" Style="{StaticResource MyTreeViewItem}">
                        <ContentPresenter Content="{Binding twolines}" ContentTemplate="{StaticResource SchemeWrapperTemplate}" />
                    </TreeViewItem>

And data template:

            <DataTemplate x:Key="SchemeWrapperTemplate">
            <ListBox ItemsSource="{Binding schemes}" 
                     ItemTemplate="{StaticResource SchemeTemplate}"
                     SelectedItem="{Binding selected_scheme}">
                <ListBox.Style>

In other place of the program:

 <Grid Grid.Row="1">
                    <TextBlock Text="{Binding selected_scheme.path}" />
                </Grid>

And when you click on some ListBoxes then selected item not changing if you click on a yet SelectedItems.

Answer 1

New answer after you edited :

It does not make much sense to bind the same object to the SelectedItem property of two different lists that contain different elements. You have to redesign your application or you may be confronted to many problems due to this strange design in the futur.

Still, you can achieve want you want to do with a little codebehing. When the user clicks on one of your ListBox, you set the selected item of your other listbox to null. Then you will be notified when you re-click on the first listbox since the selection goes from null to something.

xaml:

<Window x:Class="WpfApplication13.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525">
    <Grid>
        <StackPanel>
            <ListBox x:Name="ListBoxViewPresenter"
                     SelectedItem="{Binding CurrentlySelectedItem}" 
                     ItemsSource="{Binding MyItemsSource}" />
            <ListBox x:Name="ListBoxViewPresenter2"
                     SelectedItem="{Binding CurrentlySelectedItem}" 
                     ItemsSource="{Binding MyItemsSource2}" />
        </StackPanel>
    </Grid>
</Window>

codebehind:

using System.Collections.Generic;
using System.Windows;
using System.Windows.Input;
using System.ComponentModel;

namespace WpfApplication13
{
    /// <summary>
    /// Interaction logic for MainWindow.xaml
    /// </summary>
    public partial class MainWindow : Window, INotifyPropertyChanged
    {
        #region INotifyPropertyChanged Members

        public event PropertyChangedEventHandler PropertyChanged;

        #endregion

        private object _currentlySelectedItem;

        public object CurrentlySelectedItem
        {
            get { return _currentlySelectedItem; }

            set
            {
                _currentlySelectedItem = value;

                if (this.PropertyChanged != null)
                {
                    this.PropertyChanged(this, new PropertyChangedEventArgs("CurrentlySelectedItem"));
                }
            }
        }

        private List<int> _myItemsSource = new List<int> { 1, 2 };

        private List<int> _myItemsSource2 = new List<int> { 3, 4 };

        public List<int> MyItemsSource
        {
            get { return _myItemsSource; }
            set { _myItemsSource = value; }
        }


        public List<int> MyItemsSource2
        {
            get { return _myItemsSource2; }
            set { _myItemsSource2 = value; }
        }

        public MainWindow()
        {
            InitializeComponent();

            this.DataContext = this;

            ListBoxViewPresenter.PreviewMouseDown += ListBoxViewPresenter_PreviewMouseDown;
            ListBoxViewPresenter2.PreviewMouseDown += ListBoxViewPresenter2_PreviewMouseDown;
        }

        void ListBoxViewPresenter_PreviewMouseDown(object sender, MouseButtonEventArgs e)
        {
            ListBoxViewPresenter2.SelectedItem = null;
        }

        void ListBoxViewPresenter2_PreviewMouseDown(object sender, MouseButtonEventArgs e)
        {
            ListBoxViewPresenter.SelectedItem = null;
        }
    }
}