In a previous paper, conditions have been given to compute iterated expectations of fuzzy random variables, irrespectively of the order of integration. In another previous paper, a generalized real-valued measure to quantify the absolute variation of a fuzzy random variable with respect to its expected value have been introduced and analyzed. In the present paper we combine the conditions and generalized measure above to state an extension of the basic Rao-Blackwell Theorem. An application of this extension is carried out to construct a proper unbiased estimator of the expected value of a fuzzy random variable in the random sampling with replacement from a finite population.