The phrase "any time when" suggests a flexible or unspecified time frame. You can replace it with synonyms such as "whenever," "at any moment," "at any period," "at any point," and "at any hour." For instance, you can say "whenever you need me, I'll be there," or "at any moment, the weather may change." These synonyms for "any time when" give you more freedom and flexibility when expressing ideas or thoughts that involve an uncertain or indefinite time frame. Using them in your writing or speaking will make your sentence sound more concise and purposeful while conveying the intended meaning effectively.