@mikekaganski  , thank you for your comment.
Version 2.
' lang:en
' Returns the value of accessible property propName of obj object or Empty.
Function GetAccessibleProperty(ByVal obj As Object, ByVal propName As String)
  If Not HasUnoInterfaces(obj, "com.sun.star.accessibility.XAccessibleContext") Then
    If HasUnoInterfaces(obj, "com.sun.star.accessibility.XAccessible") Then
      obj = obj.AccessibleContext
    Else
      Exit Function        
    End If  
  End If
  
  On Error GoTo ErrLabel
  GetAccessibleProperty=CallByName(obj, propName, 2)    
ErrLabel:  
End Function
' lang: en
' Finds the top-level window by value of AccessibleID property.
Function GetDialogWindowByID(ByVal AccessibleId As String) As Object
  Dim oToolkit as Object
  Dim k As Long
  Dim oWin as Object
  
  oToolkit = Stardesktop.ActiveFrame.ContainerWindow.Toolkit
  For k = 0 To oToolkit.TopWindowCount - 1
    oWin = oToolkit.getTopWindow(k)
    If HasUnoInterfaces(oWin, "com.sun.star.awt.XDialog") Then
      If GetAccessibleProperty(oWin, "AccessibleId") = AccessibleId Then
        GetDialogWindowByID=oWin
        Exit Function
      End If
    End If
  Next k
End Function 
Sub Test
  Dim oWin as Object
  oWin = GetDialogWindowByID("SpellingDialog") ' Or "OptionsDialog", "FindReplaceDialog", ...
  If Not (oWin is Nothing) Then
    Msgbox "Found dialog with title: " & oWin.Title & Chr(10) & _
           "Description:" & Chr(10) &  GetAccessibleProperty(oWin, "AccessibleDescription")
  Else
    Msgbox "Dialog not found"
  End If  
End Sub