Modules (resp. rings) with flat socles are called FS-modules (resp. FS-rings) which are preserved by Morita equivalences and (almost) excellent extensions. One result of Xue Weimin [7] is generalized. We show that when $S$ is an almost excellent extension of $R$, if either ring is (i) left SF-ring, or (ii) right coherent, or (iii) left semi-hereditary, or (iv) left perfect, then so is another. This answers a question of Xue Weimin [8] in the affirmative.