The Boolean rank of a nonzero m $m{ imes}n$ Boolean matrix A is the least integer k such that there are an $m{ imes}k$ Boolean matrix B and a $k{ imes}n$ Boolean matrix C with A = BC. In 1984, Beasley and Pullman showed that a linear operator preserves the Boolean rank of any Boolean matrix if and only if it preserves Boolean ranks 1 and 2. In this paper, we extend this characterization of linear operators that preserve the Boolean ranks of Boolean matrices. We show that a linear operator preserves all Boolean ranks if and only if it preserves two consecutive Boolean ranks if and only if it strongly preserves a Boolean rank k with $1{leq}k{leq}min{m,n}$.