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This is what the book has to say:
To ensure that it played its part in the defence against the Red Army, Hungary was militarily occupied by the Wehrmacht on 19 March 1944. Within weeks, the possibility of employing hundreds of thousands or Hungarian Jews for war work was being excitedly discussed in the Fuehrer headquarters. The first priority for the allocation of Jewish labour were Kammler's gigantic underground building sites, but given the emergency facing the Luftwaffe the possibility of employing Jews in aircraft factories was no longer ruled out. Eichmann began the deportation of Hungarian Jewry, at the rate of 12,000-14,000 per day, in mid-May. According to the familiar principle of 'Selektion', the majority would be gassed. However, at least a third were expected to be suitable for forced labour in the Reich. Auschwitz was to serve as the 'collecting camp' for the incoming transports. Those chosen for work were to be allocated directly to Sauckel, the Todt construction organization, or other high-priority employers, such as the Jaegerstab. It is estimated that of the 509,000 Jews eventually deported from Hungary, more than 120,000 survived the war as forced labourers. In the Jaegerstab, the employment of Hungarian Jews was discussed first on 26 May 1944, the first meeting attended by the rejuvenated Albert Speer. The Jaegerstab was anxious to know what number of Jews they could expect and heard a report from an official who was clearly in regular contact with Auschwitz. With Eichmann's transport operation eleven days old, the news from the camp was not good. From the first arrivals, the Armaments Ministry had been offered only 'children, women, and old men with whom very little can be done'. The best male labour, it seems, was being retained in Hungary, digging tank traps for the Wehrmacht. The minute concluded laconically that: 'Unless the next transports bring men of an age fit for work, the whole action will not have much success.' At this stage in the war nobody can really have been in any doubt about the fate of those Jews who were not considered fit for employment. But that did not concern Speer or the Jaegerstab. A month later the flow of human material was improving and the Jaegerstab was pleased to learn that Auschwitz was now ready to make good on its promises. In particular, the SS were hoping to deliver '13,000 Hungarian Jewesses in batches of 500. Thus the smaller firms, too, will be in a position to employ these concentration camp Jewesses better. (p. 630-631)
The notes for this are 24 to 28:
24 C. Gerlach and G. Aly, Das letzte Kapitel: Der Mord an den ungarischen Juden (Stuttgart,
2002), 163-71.
25 Eichholtz, III. 239.
26 Orth gives the somewhat different figures of 458,000 deportations to Auschwitz from Hungary and 350,000 gassings. See Orth, Das System, 256-7.
27 Milch Case, II. 555. Jaegerstab conference, 26 May 1944, NOKW-336.
28 Milch Case II. 557-8, Jaegerstab conference, 27 June 1944, NOKW-359. This same group is also referred to in the Speer Chronik though they are not identified as Jews, see BAL R3/1739, June 1944, 137.
The conclusion also mentions that In the summer of 1944, Speer and the Jaegerstab maintained
a telephone hotline to the ramp at Auschwitz (p.671)