^ I had that thought too, but my other thought might be to simply show why Hitler's policies are idiotic. Tanzania, Cameroon and Namibia all have plentiful natural resources, perhaps Lettow-Vorbeck would have said "OK Adolf, you don't want the Jews in Europe? Send them here, ya racist jackass."
Hence, by the time of Kristallnacht, just about all of Germany's half million or so Jews have gone to Africa, split about 40/40/20 between Southwest Africa, German East Africa and Kamerun. This inspires recession-hammered Europeans in all of the colonial powers where their superiority is assured (i.e. - British to their colonies in British East Africa and Rhodesia, Portuguese to Angola and Mozambique, French to Malagasy and much of West Africa).
Hitler grows to be insanely despotic, but he knows that in Africa and among the Germans in Africa Lettow-Vorbeck has stature that Hitler would have a hard time touching. The Jews tossed out of Africa doesn't bother Hitler - it's cheaper to take their stuff than kill them.
After Munich, when the world has had its full of Hitler, Lettow-Vorbeck declares the German Colonies in Africa the African Federation and makes them independent of Germany. Hitler by now has a huge army but doesn't hope to have the amphibious capacity to drop an army thousands of miles away, so he can't do much about it. Lettow-Vorbeck's Free Germans and Askaris fight with the Allies. The much-increased European populations in other African colonies leads to many different squadrons of the Allies, including a British African Army (The King's African Army) and divisions from several of the allies.
During the war, Hitler's genocide becomes obvious, and Jews flee into the Soviet Union. Stalin doesn't really want them either, and so they in a great many cases use the USSR as a mere stopover, bound for someplace else. They have few options, and Africa is the better one to most.
Efforts start shortly after the war to improve the education and reduce the prejudice towards black Africans in the colonies of all the colonies, as well as the African Federation. Ravaged post-war Europe is such a mess that Africa is appealing to a great Many Brits, French, Germans and Portuguese head off to the colonies between 1945 and 1960ish.
After the war, the efforts of the Askaris and Jews leads to a growing program to educate and improve the lives of black Africans in the Federation, which remains white-ruled until the early 1970s. This forces similar efforts in the other colonial powers' as well.
Rhodesia, unified as one entity, becomes a commonwealth partner in 1955 and an independent nation in 1959. Ghana becomes independent in 1957, Kenya follows in 1960, Nigeria and others in the 1960s. Portugal chooses a different route, offering to make Angola and Mozambique full overseas territories of Portugal. This happens in 1957, but the colonies become independent completely in 1975 after the revolution in Lisbon.
The African Federations' educated peoples and increasingly intelligent workforce begins to take advantage of their natural resources, particularly in the Tanganiyka and Namibia provinces. The discovery of diamonds in 1954 leads to growth speeding up.
By 1960, the white population of Africa numbers just a hair over 20 million, about 2/5 of which live in South Africa. The Federation has 3.1 million white members, over half of which are of Jewish descent. German is the predominant language in the Federation, which is now at 75% literacy rate and climbing.
Rhodesia is the first African nation with a significant white minority to move towards majority rule, their first all race elections (with multiple voter rolls) happening in 1966. Rhodesia eases into majority rule by the early 1980s.
The Federation is led by Lettow-Vorbeck until his death in 1964. His death sets off a major power struggle, but democracy prevails here. The first elections in 1965 are only for whites and Askari military members, but this spreads to educated blacks in 1970 and eventually to full majority rule in 1980.
South Africa's infamous apartheid gets off the ground, but doesn't last long. By the early 1960s, the apartheid system (such as it is) is crumbling. Like the other African nations, majority rule comes to be by the early 1980s.
Africa in 2009 here is much, much better off than OTL. The Federation and South Africa are close to first world status, Rhodesia, Kenya, Uganda and the Portuguese colonies are at mid-level or so, comparable to Argentina or Brazil today. AIDS appears in the 1980s and is still a scourge, but it kills far less people than in OTL. Waterbourne diseases have been all but eradicated. The wealthier nations have long ago began helping the brutally held Congolese territories for economic, health and security reasons. Narrow-gauge railways and paved highways link all of the major nations of Sub-Saharan Africa.