Would you say that Husserl changed his view as regards psychologism because of criticism of Frege or was their an inkling of Husserl's later thought evidenced in the early work such as Phil of Arithmetic?

In the 1880's Husserl worked as a mathematician. This period of his development culminated in his early philosophy of mathematics, specifically of number, in Philosophy of Arithmetic, published in 1891. In this work, following Franz Brentano's empirical psychology, Husserl developed an analysis of the mental operations involved in dealing with numbers. The analysis has often been glossed as an immature exercise in psychologism, seeking to reduce mathematical truth to patterns of mental activity. Yet this was never Huserl's goal. In the Investigations he would analyze, much more clearly, forms of meaning in mental acts that represent or are directed toward typically independent objects, be they numbers or physical objects.