  The nonequilibrium fluctuation relation is a cornerstone of quantum
thermodynamics. It is widely believed that the system-bath heat exchange obeys
the famous Jarzynski-W\'{o}jcik fluctuation theorem. However, this theorem is
established in the Born-Markovian approximation under the weak-coupling
condition. Via studying the energy exchange between a harmonic oscillator and
its coupled bath in the non-Markovian dynamics, we establish a generalized
quantum fluctuation theorem for energy exchange being valid for arbitrary
coupling strength. The Jarzynski-W\'{o}jcik fluctuation theorem is recovered in
the weak-coupling limit. We also find the average energy exchange exhibits rich
nonequilibrium characteristics when different numbers of system-bath bound
states are formed, which suggests a useful way to control the quantum heat.
Deepening our understanding of the fluctuation relation in quantum
thermodynamics, our result lays the foundation to design high-efficiency
quantum heat engines.
