Eliminate transient loss of power due to inverter (UPS) transfer time
Either your receiver is very sensible for 15ms getting not power supply or switching back to mains induces too high power pulses, and your amp is going into protection mode. Here a overvoltage protection could help.
A capacitor is short circuit for AC. Don't you a capacitor as buffer for AC. Only for DC. I'd recommend an overvoltage protection or another UPS.