Wirelesslyrics send signal from proximity switch

So I am working on a project and have 12v power at two separate points and I am looking to set off a buzzer using a proximity sensor. I would like to send the signal from the proximity sensor to the buzzer wirelessly. Is there a cost effective and simple way to do this? I am very new to this type of stuff.

This: https://www.adafruit.com/products/1098

and this: https://www.adafruit.com/products/1392

I’m really surprised SF doesn’t carry the keyfobs.

So how could I replace the fob with a trasmitter assuming the receiver is attached to the buzzer?

The fob is the transmitter! or rather, it contains one.

So I bought a proximity sensor and it creates the signal when there is nothing in front of it. I need the opposite I need the signal to come when something comes in front of it. What do I need to buy?