Depends on which country (assuming African-Americans don’t just disperse throughout the continent) and why they’re migrating.
I think the most fun (but least realistic) scenario has the following criteria:
All African-Americans are migrating of their own free will, and aren’t being forced to leave/flee America
One African country decides to take all of them in and integrate them as full citizens
Gonna pick two countries for this: Ghana and Nigeria. Why? Amusement mostly.
So first: Ghana
Same rules apply: willing migration, willing integration.
Things are more “interesting” here I think, but with less conclusive answers.
My understanding of Nigerian politics is that the country tries to establish a very delicate balance between its major ethnic groups, and between Christians and Muslims. At around 219 million people, establishing such a balance isn’t easy.
So imagine the good times that will come when an enormous foreign ethnic group of 41 million people, overwhelmingly Christian, just show up.
As far as I can find, the largest ethnic group in Nigeria are the Hausa, at 65 million. Second largest are the Igbo at nearly 34 million.
So unlike the Ghana case, African-Americans wouldn’t be strolling in as the biggest guys on the block. Instead, we’d be going into an extremely competitive environment as a large-but-not-overwhelmingly-so ethnic group.
Given that whole “delicate balancing act” Nigeria does, I don’t think the Nigerian government would have a great time either. Balances would be thrown very much “out of whack.” I am not sure how exactly Abuja would reform itself to deal with it.
I hear that land is also kind of an issue in Nigeria.
I don’t think the central government has the power to override a group and “encourage” a settlement effort like Ghana might be able to in this scenario. So I think that here African-Americans might opt to stay in major cities like Lagos or Abuja, rather than risk getting entangled in land disputes that they can’t really win. That brings a different set of problems, but it might be a somewhat easier set of problems.
The good thing is, Nigeria is a large economy. So there might be more economic opportunities there than in Ghana. But the landscape would be more difficult.
More risk more reward, let’s say.
As far as America, well.
Losing 40+ million citizens has never been good for a country.
All in all, it depends.
I sometimes find the idea amusing, if extremely unlikely.