[TiammatMX]

Me encantan los diálogos de sordos, es decir, ya encontré la respuesta...

Código Delphi [-]
procedure TCopyPasteDemo.CopyButtonClick(Sender: TObject);
var
  Svc: IFMXClipboardService;
  Image: TBitmap;
begin
  if TPlatformServices.Current.SupportsPlatformService(IFMXClipboardService, Svc) then
    if TextRadioButton.IsChecked then
      Svc.SetClipboard(Edit1.Text)
    else
    begin
      Image := TextBorder.MakeScreenshot;
      try
        Svc.SetClipboard(Image);
      finally
        Image.Free;
      end;
    end;
end;

procedure TCopyPasteDemo.PasteButtonClick(Sender: TObject);
var
  Svc: IFMXClipboardService;
  Value: TValue;
  Bitmap: TBitmap;
begin
  if TPlatformServices.Current.SupportsPlatformService(IFMXClipboardService, Svc) then
  begin
    Value := Svc.GetClipboard;
    if not Value.IsEmpty then
    begin
      if Value.IsType<string> then
      begin
        PasteLabel.Text := Value.ToString;
        PasteImage.Bitmap := nil;
      end
      else if Value.IsType then
      try
        PasteLabel.Text := string.Empty;
        Bitmap := TBitmap.Create;
        try
          Bitmap.Assign(Value.AsType);
          PasteImage.Bitmap := Bitmap;
        finally
          Bitmap.Free;
        end;
      finally
        Value.AsType.Free;
      end;
    end;
  end;
end;

Ahora, a experimentar que sirva...