[NumLock]

Код:

uses
  ShellAPI;

function SHCopyFile(ExistingFileName: string; NewFileName: string): Boolean;
var
  FileOp: TSHFileOpStruct;
begin
  if GetFileAttributes(
    PChar(NewFileName+ExtractFileName(ExistingFileName))
  )=INVALID_FILE_ATTRIBUTES then
  begin
    ZeroMemory(@FileOp, SizeOf(TSHFileOpStruct));
    FileOp.wFunc:=FO_COPY;
    FileOp.pFrom:=PChar(ExistingFileName+#0);
    FileOp.pTo:=PChar(NewFileName+#0);
    FileOp.fFlags:=FOF_SILENT;
    Result:=SHFileOperation(FileOp)=0;
  end else Result:=True;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  {
    Lines.Strings = (
      'd:\CommonFiles\src\1.txt'
      'd:\CommonFiles\src\2.txt'
      'd:\CommonFiles\src\3.txt'
      'd:\CommonFiles\src\4.txt')
  }
  while Memo1.Lines.Count>0 do
  begin
    if not SHCopyFile(Memo1.Lines[0], 'd:\CommonFiles\dst\') then RaiseLastOSError;
    Memo1.Lines.Delete(0);
  end;
end;