convert mono to stereo from a karaoke unit?

Hi all, I know this is not really related to computer audio but not sure which subforum would this fit under.  

I am a newbie trying to set up a cheap karaoke system for my mom. So I have purchased this device: Fifine UHF Dual Channel Wireless Handheld Microphone.

 https://www.amazon.com/gp/product/B01N6448Q4/ref=ask_ql_qh_dp_hza

So this is my set up: one input is the microphone (which is built-in wireless microphone that comes with the unit), one input is music from the computer, the karaoke unit will mix them and output them via two outputs. The input part is fine as far as I can tell. the problem is the output.

 

The karaoke has two separate outputs: one 1/4 inch and one 1/8 inch, and each is labeled as R+L output. I originally thought it automatically means stereo output but I just discover that both outputs are just mono, so when I just connects a regular 3.5mm to 2 RCA cables, only one RCA end carries the sound (I'm kind of wondering what is the unit supposed to connect to that only accepts mono?)

 

So I am wondering what is the proper way to convert the signal to stereo? I heard of something called EPA to stereo adapter but I believe it just converts one mono to two mono with some distortion.

I’m planning to connect one output to the amplifier (which has left and right RCA inputs) and the other output back into the computer’s mic in to record (using software like audacity which right now can only records as mono).

Many thanks for reading this!