That code is pretty awful. Try:
Sub XferHeadingRange()Application.ScreenUpdating = False
Dim DocSrc As Document, RngSrc As Range
Dim DocTgt As Document, RngTgt As Range
Set DocTgt = ActiveDocument
With Application.Dialogs(wdDialogFileOpen)
  If .Show = -1 Then
    .AddToMru = False
    .ReadOnly = True
    .Visible = False
    .Update
    Set DocSrc = ActiveDocument
  End If
End With
If DocSrc Is Nothing Then Exit Sub
With DocSrc.Range
  With .Find
    .ClearFormatting
    .Replacement.ClearFormatting
    .Text = "SOURCE SECTION HEADING EXAMPLE"
    .Replacement.Text = ""
    .Forward = True
    .Wrap = wdFindStop
    .MatchWildcards = False
    .Execute
  End With
  If .Find.Found = True Then
    Set RngSrc = .Paragraphs(1).Range
    Set RngSrc = RngSrc.GoTo(What:=wdGoToBookmark, Name:="\HeadingLevel")
  Else
    MsgBox "Source Content Not Found!", vbExclamation
    GoTo CleanUp
  End If
End With
With DocTgt.Range
  With .Find
    .ClearFormatting
    .Replacement.ClearFormatting
    .Text = "TARGET SECTION HEADING EXAMPLE"
    .Replacement.Text = ""
    .Forward = True
    .Wrap = wdFindStop
    .MatchWildcards = False
    .Execute
  End With
  If .Find.Found = True Then
    Set RngTgt = .Paragraphs(1).Range
    RngTgt.Collapse wdCollapseStart
    RngTgt.FormattedText = RngSrc.FormattedText
  Else
    MsgBox "Destination Not Found!", vbExclamation
  End If
End With
: CleanUp
DocSrc.Close SaveChanges:=False
Set RngSrc = Nothing: Set DocSrc = Nothing
Set RngTgt = Nothing: Set DocTgt = Nothing
Application.ScreenUpdating = True
End Sub
Note: The code assumes the target document is already open and that Word's Heading Styles are used in the source document to denote the various ranges. When running the macro, you select the source document to open from the dialog box. For the target document, the heading to specify is the one after the location where you want the source content inserted.