I have been able to resolve the problem with the following changes to the class:

Code:
Imports System
Imports System.IO
Imports System.Text
Imports System.Security.Cryptography

Public Class SHA

    Public Shared Function GenerateSHA512String(ByVal inputString As String) As String
        Using SHA512 As SHA512 = SHA512Managed.Create()

            Using fileStream As FileStream = File.OpenRead(inputString)
                Return BitConverter.ToString(SHA512.ComputeHash(fileStream)).Replace("-", "").ToLowerInvariant()
            End Using

        End Using
    End Function

End Class
Now, the hash generated is the same hash as shown when using certutil.exe.