The reduced state of a small system strongly coupled to a charger in thermal equilibrium may be athermal and used as a small battery once disconnected. By harnessing the battery-charger correlations, the battery's extractable energy can increase above the ergotropy. We introduce a protocol that uses a quantum system as a memory that measures the charger and leaves the battery intact in its charged state. Using the information gained from the measurement, the daemonic ergotropy of the battery is extracted. Then the battery is reconnected to the charger, thermalizing and charging it. However, the memory should return to its initial standard state to close the thermodynamic cycle. Thus, on the one hand, the work cost of the cycle is the sum of the disconnecting and reconnecting battery-charger work plus the measurement and erasure work. On the other hand, the extracted energy is the daemonic ergotropy of the battery plus the ergotropy of the memory. The ratio of these quantities defines the efficiency of the cycle. The protocol is exemplified by a modified transverse spin 1/2 Ising chain, one spin functioning as the battery and the others as the charger. The memory is another auxiliary spin 1/2. We found pairs of measurement schemes from which we extract the same daemonic ergotropy from the battery, they dissipate the same amount of energy, and one leaves the memory in an active state, the other in a passive state. We study the memory's ergotropy and the daemonic ergotropy of the battery. We find that with measurements, the efficiency can surpass that of the unmeasured protocol, given conditions on temperature, coupling, and choice of the measurement operators.