  A Fully Many-Body Localized (FMBL) quantum disordered system is characterized
by the emergence of an extensive number of local conserved operators that
prevents the relaxation towards thermal equilibrium. These local conserved
operators can be seen as the building blocks of the whole set of eigenstates.
In this paper, we propose to construct them explicitly via some block
real-space renormalization. The principle is that each RG step diagonalizes the
smallest remaining blocks and produces a conserved operator for each block. The
final output for a chain of $N$ spins is a hierarchical organization of the $N$
conserved operators with $\left(\frac{\ln N}{\ln 2}\right)$ layers. The
system-size nature of the conserved operators of the top layers is necessary to
describe the possible long-ranged order of the excited eigenstates and the
possible critical points between different FMBL phases. We discuss the
similarities and the differences with the Strong Disorder RSRG-X method that
generates the whole set of the $2^N$ eigenstates via a binary tree of $N$
layers. The approach is applied to the Long-Ranged Quantum Spin-Glass Ising
model, where the constructed excited eigenstates are found to be exactly like
ground states in another disorder realization, so that they can be either in
the paramagnetic phase, in the spin-glass phase or critical.
