Try the following macro.
Notes:
1. None of the hyperlinks in your document are in paragraphs using the Heading 1 Style - they use a variety of other styles.
2. Some paragraphs have multiple hyperlinks, so only the first one is processed.
3. As coded, the macro adds the new hyperlink to the first word in the paragraph (i.e. the word after the paragraph's #).
Code:
Sub Demo()
Application.ScreenUpdating = False
Dim RngDoc As Range, RngLnk As Range, HLnk As Hyperlink, StrAddr
With ActiveDocument
Set RngDoc = .Range: Set RngLnk = .Range(0, 0)
If .TablesOfContents.Count > 0 Then
RngDoc.Start = .TablesOfContents(.TablesOfContents.Count).Range.End
End If
End With
For Each HLnk In RngDoc.Hyperlinks
If HLnk.Range.Paragraphs(1).Range <> RngLnk Then
Set RngLnk = HLnk.Range.Paragraphs(1).Range
With RngLnk
StrAddr = .Hyperlinks(1).Address
HLnk.Range.Fields(1).Unlink
.Hyperlinks.Add Anchor:=.Words.First, Address:=StrAddr, TextToDisplay:=.Words.First.Text
End With
End If
Next
Application.ScreenUpdating = True
End Sub