The use of generative artificial intelligence (GenAI) in the educational and research activities of university stakeholders is not inherently a violation of academic integrity. However, the output of AI may contain violations of academic integrity. This chapter explores two questions: “How can AI be used in educational and research activities in honest way?” and “How familiar are university stakeholders with the dangers of using AI in their educational and research activities?” We analyze the functioning of AI as a tool for a non-specialist user. First, we investigate ways to avoid violations of academic integrity when creating a text product in a dialogue mode with AI. We gave ChatGPT several tasks that “reveal” its shortcomings, including the fabrication of a list of references, lack of references in the text, incorrect use of the Creative Commons license, recognition of text authorship, and distortion of facts. The dialogue is conducted from the perspectives of students and teachers. We analyze each response and provide recommendations for AI users designing prompts. Second, we analyze the results of a survey of Ukrainian academics awareness of possible violations of academic integrity in texts created by AI. The survey highlights the main challenges with AI in educational and scientific texts.