  Quantum coherence represented by a superposition of energy eigenstates is,
together with energy, an important resource for quantum technology and
thermodynamics. Energy and quantum coherence however, can be complementary. The
increase of energy can reduce quantum coherence and vice versa. Recently, it
was realized that steady-state quantum coherence could be autonomously
harnessed from a cold environment. We propose a conditional synthesis of $N$
independent two-level systems (TLS) with partial quantum coherence obtained
from an environment to one coherent system using a measurement able to increase
both energy and coherence simultaneously. The measurement process acts here as
a Maxwell demon synthesizing the coherent energy of individual TLS to one large
coherent quantum battery. The measurement process described by POVM elements is
diagonal in energy representation and, therefore, it does not project on states
with quantum coherence at all. We discuss various strategies and their
efficiency to reach large coherent energy of the battery. After numerical
optimization and proof-of-principle tests, it opens way to feasible
repeat-until-success synthesis of coherent quantum batteries from steady-state
autonomous coherence.
