Well, the message is accurate, there is no entry point named "AppendMenu" in user32.dll. It actually has two versions of it. One is named AppendMenuA, the A means Ansi. The legacy version that uses 8-bit encoded strings, commonly used in old C programs. And AppendMenuW, the W means Wide. It takes a Unicode string like all winapi functions do on modern Windows versions.
Your old-style Declare statement is using the legacy function. You should use the Alias keyword to give the proper entrypoint name:
Private Declare Function AppendMenu Lib "user32.dll" Alias "AppendMenuA" (ByVal hMenu As IntPtr, ByVal uFlags As Int32, ByVal uIDNewItem As IntPtr, ByVal lpNewItem As String) As Boolean
Or just plain call it AppendMenuA. Using the legacy function isn't very pretty, although it won't have a problem converting "About" to Unicode. But do favor the modern way to declare pinvoke functions, it has many advantages beyond automatically mapping to the A or W version:
Imports System.Runtime.InteropServices
Imports System.ComponentModel
...
<DllImport("user32.dll", CharSet:=CharSet.Auto, SetLastError:=True)> _
Private Shared Function AppendMenu(ByVal hMenu As IntPtr, ByVal uFlags As Int32, ByVal uIDNewItem As IntPtr, ByVal lpNewItem As String) As Boolean
End Function
...
If Not AppendMenu(hSysMenu, MF_STRING, IntPtr.Zero, "About") Then
Throw New Win32Exception()
End If