Solved! Connecting wirelessly the projector's audio to the amplifier.

Solution
Yes a bluetooth adapter should work. For connecting it wirelessly to the PC, same exact way, you can get wireless video adapters for HDMI, etc.. to connect them. Just keep in mind that they have distance and probably line of sight limitations.
Yes a bluetooth adapter should work. For connecting it wirelessly to the PC, same exact way, you can get wireless video adapters for HDMI, etc.. to connect them. Just keep in mind that they have distance and probably line of sight limitations.
 
Solution