string filterCellValue = "";
private void RadVirtualGrid1_EditorRequired(object sender, VirtualGridEditorRequiredEventArgs e)
{
    if (e.Editor is VirtualGridTextBoxEditor textBoxEditor)
    {

        var virtualGridFilterRowElement = this.radVirtualGrid1.TableElement.ViewElement.TopPinnedRows.Children[2];
        VirtualGridFilterCellElement filterCellElement = virtualGridFilterRowElement.Children[2].Children.FirstOrDefault(x  => (x as  VirtualGridFilterCellElement).ColumnIndex == e.ColumnIndex) as VirtualGridFilterCellElement;
        if (filterCellElement != null)
        {
            filterCellValue = filterCellElement.Text;
        }
    }
}

private void RadVirtualGrid1_CellEditorInitialized(object sender, VirtualGridCellEditorInitializedEventArgs e)
{
    var textBoxEditor = e.ActiveEditor as VirtualGridTextBoxEditor;
       
    if (filterCellValue != "")
    {
        textBoxEditor.Value = filterCellValue;
    }  
}