using SelectedValue and SelectedValuePath.
The TreeViewItem child and parent must have the same Uid.
<Window x:Class="WpfApp1.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<StackPanel>
<TreeView x:Name="treeView" Height="200" SelectedValuePath="Uid">
<TreeViewItem Header="Letters-1" x:Name="tab1" Uid="Letters-1">
<TreeViewItem Header="a" Uid="Letters-1"/>
<TreeViewItem Header="b" Uid="Letters-1"/>
<TreeViewItem Header="c" Uid="Letters-1"/>
</TreeViewItem>
<TreeViewItem Header="Letters-2" x:Name="tab2" Uid="Letters-2">
<TreeViewItem Header="d" Uid="Letters-2"/>
<TreeViewItem Header="e" Uid="Letters-2"/>
<TreeViewItem Header="f" Uid="Letters-2"/>
</TreeViewItem>
<TreeViewItem Header="Letters-3" x:Name="tab3" Uid="Letters-3">
<TreeViewItem Header="g" Uid="Letters-3"/>
<TreeViewItem Header="h" Uid="Letters-3"/>
<TreeViewItem Header="i" Uid="Letters-3"/>
</TreeViewItem>
</TreeView>
<TabControl x:Name="tabControl" Height="100"
SelectedValuePath="Header"
SelectedValue="{Binding ElementName=treeView, Path=SelectedValue, Mode=OneWay}">
<TabItem Header="Letters-1"/>
<TabItem Header="Letters-2"/>
<TabItem Header="Letters-3"/>
</TabControl>
</StackPanel>
</Window>
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solved WPF C# Bind multiple treeViewItems isSelected to tabItem isSelected