Artificial intelligence (AI) is increasingly promoted as a means of enabling small and medium-sized enterprises (SMEs) to enter foreign markets, yet technology adoption alone does not create export readiness. This article develops a capability-based explanation of how African entrepreneurial SMEs can convert AI resources into dependable cross-border operating capacity under the African Continental Free Trade Area (AfCFTA). A structured, theory-building integrative review combined six multidisciplinary academic-index searches with targeted publisher and institutional searches. Sixty-nine unique records were screened, 47 complete records were assessed, and 37 evidence items were retained. The synthesis integrates the resource-based view, dynamic capabilities, technology-organisation-environment reasoning, operations capability theory, institutional theory and responsible-AI principles. Findings indicate that AI contributes to export readiness only when assimilated into routines for market intelligence, process and quality reliability, supply-chain visibility, standards compliance, pricing and finance, organisational learning and human oversight. Data quality, managerial interpretation, workflow redesign and cross-functional coordination constitute the principal conversion mechanisms, while infrastructure, finance, skills, sector, firm size and institutional implementation condition their effects. The resulting AI-Enabled Export Operations Capability framework distinguishes AI adoption, assimilation, operations capability, responsible export readiness and realised export performance. It extends digital entrepreneurship and SME internationalisation research by positioning responsible operational capability, rather than technology ownership, as the central mechanism linking AI to cross-border entrepreneurial action.