Generative AI, including Large Language Models (LLMs), is integrated into societal contexts in Africa, including in higher education. Many students, teachers, and educational administrators use these technologies daily for various purposes. This paper examines the opportunities and challenges of integrating generative AI into the higher education systems in Africa. The discussion is grounded in practical testing of TurkuEval at the University of Namibia. This LLMbased platform allows students to study learning materials, answer related questions, and receive AI-generated grading and feedback on their responses. Teachers can review and validate the AI's grading and feedback, thus creating a complementary approach for using LLMs in higher education. Pre-evaluation, evaluation, and postevaluation steps are essential to ensure a systematic and secure LLM use for evaluating students' written work. Leveraging the benefits of generative AI in African higher education requires broader policies, clear instructions and transparent explanations of results to reduce algorithmic aversion and prevent misuse or rejection of LLM technologies in education.