I asked one of the most experienced researchers I know – Larry deZeng. Here is his reply:
Infanterie-Division Ulrich von Hutten. "*Formed 30 March 1945 in Wittenberg/Wehrkreis IV as a division of the 35th Wave from personnel gathered from schools and replacement units located in various Wehrkreise. Organized as an Infanterie-Division 45, the assembly and formation of the Division continued until 25 April 1945. Designated as a GIF (Generalinspekteur für die Führernachwuchs-) Division. For the formation of the artillery component, V.Abt./Volks-Artillerie-Korps 412 was used."
*Tessin, Georg. Verbände und Truppen der deutschen Wehrmacht und Waffen-SS im Zweiten Weltkrieg 1939-1945. 16+ Bde. Osnabrück: Biblio Verlag, 1965-c.1990. Band. XIV, pp.244-45.
Tessin lists the components of the Division and where it was engaged, but he wrote nothing about the origin of the Stab. If available, the Division's formation orders should be in the surviving records of the Organisations-Abt./OKH and these are on microfilm at NARA in RG 242/Microcopy T-78. These should definitively reveal the origin of the Stab.