Why don't you open both source and target file in binary mode?

Code:
Dim Data As String
Dim FileName As String
Dim BSize As Long
Dim fSz As Long

FileName = InputBox("Enter filename.", "Save")
If FileName <> "" Then
    'Set the buffer size
    BSize = 4096
    Open App.Path & "\Controls.cont" For Binary Access Read As #1
    Open App.Path & "\" & FileName For Binary Access Write As #2

    fSz = LOF(1)
    Do Until EOF(1)
        ' Don't read too much at the end.
        If fSz - Loc(1) <= BSize Then BSize = fSz - Loc(1) + 1
        
        ' Read & write the data
        Data = Space$(BSize)
        Get #1, , Data
        Put #2, , Data
        DoEvents
    Loop
    Close #1
    Close #2
    MsgBox "File copy successful.", vbInformation + vbOKOnly, "Save"
Else
    MsgBox "Please enter a valid fiilename.", vbExclamation + vbOKOnly, "Save"
End If
Yet, you also can use the VB build in FileCopy function as

Code:
Dim Source as string
dim Target as string

Source = "C:\Controls.cont"
Target = "C:\Target.txt"
FileCopy Source, Target