The contents of the paper under review provide an explicit, nice and easy example of a group which is subgroup separable but not conjugacy separable. \par A group $G$ is said to be residually finite if every nontrivial element $1\neq g\in G$ projects to a nontrivial element in some finite quotient of $G$. This notion owes its importance to Malʹtsev, who first pointed out that such groups have solvable word problem (by two simultaneous brute force and possibly infinite procedures, one of them trying to show that the given word represents the trivial element, and the other trying to show it does not). A group $G$ is said to be conjugacy separable if, for any two non-conjugate elements $g_1,\, g_2\in G$, their projections remain non-conjugate in some finite quotient of $G$. Also, $G$ is said to be subgroup separable if, for any element $g\in G$ and any finitely generated subgroup $H\leqslant G$ such that $g\not\in H$, their projections satisfy the same condition, i.e.\ $\overline{g}\not\in \overline{H}$, in some finite quotient of $G$. Again, similar brute force algorithms show that conjugacy separable groups have solvable conjugacy problem, and subgroup separable groups have solvable membership problem (also known as generalized word problem). \par The direct product of two free groups, say $F_2\times F_2$, is easily seen to be conjugacy separable but it is not subgroup separable because, by an old result due to Mihailova, it has unsolvable membership problem. So, conjugacy separability does not imply subgroup separability. The other implication was open until now, with all the known examples of subgroup separable groups being conjugacy separable as well (see a list of most of them in the paper). \par The paper under review shows that this last implication is false by providing an explicit counterexample. This example is an amalgamated free product of several finite cyclic extensions of the additive group of matrices $H=M_3(\Bbb{Z})\simeq \Bbb{Z}^9$ by certain finite order $3\times 3$ matrices $g$ of determinant 1, acting on $H$ as $a\cdot g=g^tag$, where $a\in H$. All the arguments are elementary except they make use of a result of Raptis-Talelli-Varsos characterizing subgroup separability within the family of fundamental groups of graphs of polycyclic-by-finite groups with all edge groups being of finite index in the respective vertex groups.