How to configure the projector light currently controlled by a remote (see pic of both please)

I suppose you could buy a Broadlink RM mini 3, learn the remote codes and use this component:

You’ll struggle with line of sight between any remote hub and an outdoor light (I’m presuming that’s an outdoor light). I had a remote like that for a bulb in the house and I struggled to get any kind of consistency by using my Harmony Hub to control it.

I think you’d probably be better off with a Sonoff added to the power line; it’s a cheaper option to try out and will work over WiFi so you have a better chance of connection outside.

https://www.sonoff.in/sonoff-switch