  One of the defining features of many-body localization is the presence of
extensively many quasi-local conserved quantities. These constants of motion
constitute a corner-stone to an intuitive understanding of much of the
phenomenology of many-body localized systems arising from effective
Hamiltonians. They may be seen as local magnetization operators smeared out by
a quasi-local unitary. However, accurately identifying such constants of motion
remains a challenging problem. Current numerical constructions often capture
the conserved operators only approximately restricting a conclusive
understanding of many-body localization. In this work, we use methods from the
theory of quantum many-body systems out of equilibrium to establish a new
approach for finding a complete set of exact constants of motion which are in
addition guaranteed to represent Pauli-$z$ operators. By this we are able to
construct and investigate the proposed effective Hamiltonian using exact
diagonalization. Hence, our work provides an important tool expected to further
boost inquiries into the breakdown of transport due to quenched disorder.
