const
  {uses windows for WIN or LMessages for LINUX}
  WM_ADDSTREAMPARAM_MSG = WM_USER + $101;
  WM_CONTAINERCLEAR_MSG = WM_USER + $102;


type

  TStreamRec = packed record
    ContainerType: Integer;
    ByteArray: array of Byte;
  end;

  { TMyThread }

  TMyThread = class(TThread)
  private
    FArrStreamRec: array of TStreamRec;
  protected
    procedure Execute; override;
  public
    FIsTermThread: Boolean;
    constructor Create (CreateSuspended: boolean; ArrStreamRec: array of TStreamRec);
  end;

  { TForm1 }

  TForm1 = class(TForm)
//<skiped>
  private
    FMyThread: TMyThread;
  public
    procedure WM_AddStreamParam_Msg (var Msg: TLMessage); message WM_ADDSTREAMPARAM_MSG;
    procedure WM_ContainerClear_Msg (var Msg: TLMessage); message WM_CONTAINERCLEAR_MSG;
  end; 

procedure TForm1.BtnThreadClick(Sender: TObject);
var
  msM //поток для Memo
  //, dms
  , msP: TMemoryStream; //поток для Picture

  MyStreamArr: array of TStreamRec;
begin
  if Assigned(FMyThread) then Exit;

  msM:= TMemoryStream.Create;//для строк
  //dms:= TMemoryStream.Create;
  msP:= TMemoryStream.Create;//для картинки
  try
    //    ===== MemoSrc ====
    MemoSrc.Lines.SaveToStream(msM);
    msM.Position:= soFromBeginning;

    SetLength(MyStreamArr, 2);//размер array of TStreamRec
    SetLength(MyStreamArr[0].ByteArray,msM.Size);//определяем размер массива байтов поля array of TStreamRec
    msM.Read(MyStreamArr[0].ByteArray[0],msM.Size);//читаем содержимое потока в массив поля записи
    MyStreamArr[0].ContainerType:= 0;//тип контейнера Memo

    //    ===== MemoSrc ====
    ImgSrc.Picture.SaveToStream(msP);
    msP.Position:= 0;

    SetLength(MyStreamArr[1].ByteArray, msP.Size);
    msP.Read(MyStreamArr[1].ByteArray[0],msP.Size);
    MyStreamArr[1].ContainerType:= 1;

    //создаем поток с параметрами и ждем результаты
    FMyThread:= TMyThread.Create(True,MyStreamArr);

    try
      while not FMyThread.FIsTermThread do
      begin
        Application.ProcessMessages;
        Sleep(500);
      end;
    finally
      FreeAndNil(FMyThread);
    end;

    //вот так все копируется в новый контейнер корректно
    //dms.Write(MyStreamArr[0].ByteArray[0],Length(MyStreamArr[0].ByteArray));
    //dms.Position:= soFromBeginning;
    //ImgDest.Picture.LoadFromStream(dms);
  finally
    FreeAndNil(msP);
    //FreeAndNil(dms);
    FreeAndNil(msM);
  end;
end;    

procedure TForm1.WM_ContainerClear_Msg(var Msg: TLMessage);
begin
  case Msg.wParam of
    0: begin
      MemoDest.Clear;
      Label1.Caption:= 'грузим Memo';
    end;
    1: begin
      ImgDest.Picture.Clear;
      Label1.Caption:= 'грузим картинку';
    end;
  end;
end;

constructor TMyThread.Create(CreateSuspended: boolean;
  ArrStreamRec: array of TStreamRec);
var
  i: Integer;
begin
  inherited Create(CreateSuspended);
  Priority:= tpLower;
  FreeOnTerminate:= False;
  FIsTermThread:= False;

  if Length(ArrStreamRec) > 0 then
    begin
      SetLength(FArrStreamRec,Length(ArrStreamRec));

      for i := Low(ArrStreamRec) to High(ArrStreamRec) do
        begin
          FArrStreamRec[i].ContainerType:= ArrStreamRec[i].ContainerType;
          SetLength(FArrStreamRec[i].ByteArray,Length(ArrStreamRec[i].ByteArray));//надо ли определять размер?
          FArrStreamRec[i].ByteArray:= ArrStreamRec[i].ByteArray;
        end;
    end;

  if CreateSuspended then Start;
end; 

procedure TForm1.WM_AddStreamParam_Msg(var Msg: TLMessage);
var
  ARec: TStreamRec;
  ms: TMemoryStream;
begin

  ARec:= TStreamRec(Pointer(Msg.lParam)^);

  ms:= TMemoryStream.Create;
  try
    ms.Write(ARec.ByteArray[0],Length(ARec.ByteArray));
    ms.Position:= soFromBeginning;

    case Msg.wParam of
      0: MemoDest.Lines.LoadFromStream(ms);
      1: ImgDest.Picture.LoadFromStream(ms);
    end;
  finally
    FreeAndNil(ms);
  end;
end;                                             

{ TMyThread }

procedure TMyThread.Execute;
var
  msg: TLMessage;
begin
  msg.wParam:= FArrStreamRec[0].ContainerType;
  SendMessage(Form1.Handle,WM_CONTAINERCLEAR_MSG,msg.wParam,0);//чистим контейнер (это memo)
  SendMessage(Form1.Handle,WM_ADDSTREAMPARAM_MSG,0,DWORD(@FArrStreamRec[0]));
  Sleep(2000);

  msg.wParam:= FArrStreamRec[1].ContainerType;
  SendMessage(Form1.Handle,WM_CONTAINERCLEAR_MSG,msg.wParam,0);//чистим контейнер (это Picture)
  SendMessage(Form1.Handle,WM_ADDSTREAMPARAM_MSG,0,DWORD(@FArrStreamRec[1]));
  Sleep(2000);

  FIsTermThread:= True;
end;

procedure TForm1.WM_AddStreamParam_Msg(var Msg: TLMessage);
var
  ARec: TStreamRec;
  ms: TMemoryStream;
begin

  ARec:= TStreamRec(Pointer(Msg.lParam)^);

  ms:= TMemoryStream.Create;
  try
    ms.Write(ARec.ByteArray[0],Length(ARec.ByteArray));
    ms.Position:= soFromBeginning;

    case Msg.wParam of
      0: MemoDest.Lines.LoadFromStream(ms);
      1: ImgDest.Picture.LoadFromStream(ms);
    end;
  finally
    FreeAndNil(ms);
  end;
end;