You might try plugging a bluetooth transmitter into the headphone jack of the amplifier. Some amps have 3.5mm headphone jacks, and some have 1/4" headphone jacks. If 1/4", you can use an adapter. For portability, you could plug the bluetooth transmitter, into a headphone amp.. Instead of a Bluetooth transmitter, you could try a FM transmitter instead, if your boombox device has a FM radio.

I don't know how good it will sound.