I found it. The way it works for me is
Code:
If .Find.Found = True Then
Set Rng = .Duplicate
Set Rng = Rng.GoTo(What:=wdGoToBookmark, Name:="\HeadingLevel")
Rng.Start = Rng.Paragraphs.First.Range.End
MsgBox Rng.Text
End If
The crux was the Rng.Paragraphs.First.
Range.End