Put the following in the code module for the worksheet. You said Col H
is filled in as a result of entry in another column. If so, you will
need to change the 2nd half to use the appropriate column/offsets.

Private Sub Worksheet_Change(ByVal Target As Range)

If Target.Column = 7 Then 'col G
Target.Offset(0, -6) = DateAdd("m", 1, Target)
End If
If Target.Column = 8 Then 'col H
If IsEmpty(Target.Offset(0, -1)) Then
Target.Offset(0, -7) = DateAdd("yyyy", 1, Target)
Else
Target.Offset(0, -7) = DateAdd("m", 1, Target.Offset(0, -1))
End If
End If
End Sub

Hth,
Merjet