The name 'Auslands- und Volkstumsamt' would seem to have come into existence in 1943 Mike. I've listed what I have below. Hope it is of some use.
30.9.1939 (peacetime) I can't scan this chart as my scanner isn't playing but both of the following Ämter came under
Befehlsstelle I - Einsatz
Amt A - Auslandsamt
Main departments
I. Auslandsverbindungen
II. Reichsdeutsche Jugend im Ausland
Amt GV - Grenz- und Volkspolitisches Amt
Main departments
I. Deutschtumsarbeit
II. Volkspolitische Arbeit
III. Grenzlandarbeit
25.10.1941:
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1942
Grenz- und Auslandsamt (again, my scanner isn't working but I'll try it again later)
1943
Auslands- und Volkspolitisches Amt*
*The chart shows this as the name of the Amt but in the accompanying text it is named as 'Auslands- und Volkstumsamt'.
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The attached graphic comes from the 1944 SHAEF handbook and shows a couple of names. Not always easy to interpret the data contained in that publication as the sources used aren't dated but in this case they show a K-Führer working in the department which shows that the allies had data from that period when they compiled this particular section:
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