procedure TForm1.Button1Click(Sender: TObject);
var
  Downloader: TFileDownloader;
  mstream: TMemoryStream;
begin
  mstream := TMemoryStream.Create;
  Downloader := TFileDownloader.Create('https://www.example/datei.txt', mstream);
  Downloader.OnDownloadComplete := DownloadComplete;
  Downloader.Start;
end;

unit SynchronousHttpClientStreamDownloader;

interface

uses
  System.Classes, System.SysUtils, System.Net.HttpClient, System.Net.URLClient;

type
  TDownloadCompleteEvent = procedure(const stream: TStream; Success: Boolean) of object;

  TFileDownloader = class(TThread)
  private
    FURL: string;
    FStream: TStream;
    FHttpClient: THTTPClient;
    FOnDownloadComplete: TDownloadCompleteEvent;
    FSuccess: Boolean;
    procedure DownloadFile;
    procedure DoDownloadComplete;
  protected
    procedure Execute; override;
  public
    constructor Create(const URL: String; aStream: TStream);
    destructor Destroy; override;
    property OnDownloadComplete: TDownloadCompleteEvent read FOnDownloadComplete write FOnDownloadComplete;
  end;

implementation

{ TFileDownloader }

constructor TFileDownloader.Create(const URL: String; aStream: TStream);
begin
  inherited Create(True);
  FreeOnTerminate := True;
  FURL := URL;
  FStream := aStream;
  FHttpClient := THTTPClient.Create;
end;

destructor TFileDownloader.Destroy;
begin
  FHttpClient.Free;
  inherited;
end;

procedure TFileDownloader.DownloadFile;
var
  vHTTP: THTTPClient;
begin
  try
    FStream := TMemorystream.Create; // FStream muss an dieser Stelle erzeugt werden, im Execute klappt es nicht. Free muss aber im Execute stehen
    Assert(FStream <> nil);

    vHTTP := THTTPClient.Create;
    vHTTP.CustomHeaders['Pragma'] := 'no-cache';

    try
      vHTTP.Get(FURL, FStream);
      FSuccess := True;
    finally
      vHTTP.Free;
    end;
  except
    on E: Exception do
    begin
      FSuccess := False;
    end;
  end;
end;

procedure TFileDownloader.DoDownloadComplete;
begin
  if Assigned(FOnDownloadComplete) then
  begin
    FOnDownloadComplete(FStream, FSuccess);
    FStream.Free
  end
end;

procedure TFileDownloader.Execute;
begin
  DownloadFile;
  Synchronize(DoDownloadComplete);
end;

end.