The survival game is all about adaptability to the environment. Grizzlies and Black Bears have evolved to survive in forests and will likely die in an African Savannah in a few days from starvation/dehydration/murder by local predators.
Nitpicking here, but it's about adaptability to the ecosystem, which includes the biological elements. It's not uncommon that a predator introduced to an ecosystem finds a bunch of prey who have not adapted any defenses to it, and starts killing things left and right. Hence the whole invasive species thing. Think Burmese pythons.
I think the bear would struggle with catching animals. It would probably starve
They may not need to. If we're thinking African savanna, for example, there are some places where male lions do not hunt, because game density is so high that they can always scavenge something. Spotted hyenas will defend a kill from female lions given a large enough numerical advantage, but not male lions, because the individual size disparity is so large. I can see larger bear species enjoying a similar advantage and doing quite well scavenging from smaller predators like hyenas and cheetahs.
Bears are also pretty good at digging up moths, and it would be interesting to see if they could make a living off termite mounds. Bears also do pretty well with garbage produced by humans, which is plentiful in some places.
Africa is a huge continent with varying ecosystems.
I am sure one of them could support a healthy bear population.
Just to add to this, there are also a lot of different bears. I doubt polar bears would do well in the NamibRand desert, but it's pretty unthinkable to me that no species of bear would be successful in any African ecosystem.
If you are asking how bears would do in africa.....not good. Bears are solitary creatures much like tigers, and much like tigers, they would get hunted down by pack hunters such as lions and hyenas. African animals form gangs lol. So even if you are a shit kicking fighter.....good luck against a squad. The south american rain forrest and African savanna are two of the most unforgiving places on earth as far as survivability amongst other animals.
There are plenty of solitary hunters in Africa, although most of them are smaller and avoid conflict with the bigger ones. It would be interesting to see whether lions actively hunt larger species of bears. I think they probably would, but whether they'd hunt them to extirpation, I'm not sure. Anyway, there are plenty of places in Africa without lions.
I think the bigger issues are crocodiles and snakes. Bears would likely need a lot of water to keep their temperature down and larger pools of water in Africa tend to mean crocodiles, many of which are large enough to bring down any bear, to say nothing of bear cubs. The biggest issue that's pretty much continent-wide is venomous snakes. Africa is a whole different ballgame from the Americas when it comes to venomous snakes, hence the tendency for African primates to have trichromatic vision, while American primates tend to have dichromatic or even monochromatic vision. Poor adaptation to its snakes could make it really difficult for a large mammal to thrive in most parts of Africa.