type
  TDownloadCallBackStatus = procedure(FilesDownloaded: Integer) of object;
  PDownloadCallBackStatus = ^TDownloadCallBackStatus;

  Txxx = class(T...)
  private
    {...}
  public
    {...}
    procedure DownloadOrSynchronize(SearchString: string; OnlySync: boolean;
      CallBackStatus: PDownloadCallBackStatus);
  end;

procedure Txxx.DownloadOrSynchronize(SearchString: string;
  OnlySync: boolean; CallBackStatus: PDownloadCallBackStatus);
var
begin
  {...}

  if Assigned(CallBackStatus) then
  begin
     CallBackStatus^(j); // <-- EACCESSVIOLATION
  end;

  {...}

end;

procedure CallBack(FilesDownloaded: Integer);
begin
  MainForm.label_x.Caption := inttostr(FilesDownloaded);
end;

procedure TMainForm.btn_download_click(Sender: TObject);
begin
  {...}
  AOBJ.DownloadOrSynchronize(edt_tags.Text, chk_nodownload.Checked, @CallBack);
  {...}
end;