An experimental technique for the indirect manipulation and detection of electron spins entangled in two-dimensional magnetoexcitons has been developed. The kinetics of the spin relaxation has been investigated. Photoexcited spin-magnetoexcitons were found to exhibit extremely slow relaxation in specific quantum Hall systems, fabricated in high mobility GaAs/AlGaAs structures; namely, the relaxation time reaches values over one hundred microseconds. A qualitative explanation of this spin-relaxation kinetics is presented. Its temperature and magnetic field dependencies are discussed within the available theoretical framework.