Anagram is a word, a phrase, or a sentence generated by reordering the letters of a given, another word, phrase, or sentence. People have used anagrams as a word game, pseudonym, or cryptography. In previous work which proposed an automatic generation method for Japanese anagram senteces, it is hard to incorporate user prefrence, even when a user has flash of some interesting words or phrases. Although Interactive Evolutionary Computation (IEC) is a promising approach to incorporate user preference, IEC faces the trade-off problem between search performance and cost due to user fatigue during solution evaluation. Therefore, this paper proposes a method for Japanese anagram sentence generation using Cooperative Evolution by User and System (CEUS). CEUS is a method enabling to change the search roles between a user and a system in problems involving both qualitative and quantitative objective functions. The proposed anagram generation method using CEUS allows a user to give a bias to the search, not to make much operations, and to directly incorporate good words or phrases the user thinks of during the search. Experimental results showed that, by dynamic search role changes and qualitative objective function prediction, the proposed method could generate anagram sentences more efficiently than IEC-based method with keeping good support for user's divergent thinking.