How to make a clickable moving button

[Exiscoming]

I'm making a side scrolling game where the player can randomly encounter an event along the way.
That means the encounter spawns somewhere along the path and comes into frame as you move from left to right.
Now what I want to do is make the encounter a button that you can click on.

The problem
I normally use imagebuttons, however they are part of a screen, and screens can't be animated.
Because the encounter (and the player) move around, I need to figure out a way the player can click on the encounter.

The Question
How do I make clickable buttons that move around?

Visual:
https://i.imgur.com/fpjT2r3.mp4

[Imperf3kt]

Imagebutton suit this well.

Take a look at this post which has an example project that details exactly how to do what you're asking.

viewtopic.php?f=51&t=22565&start=75#p455107

[Exiscoming]

That's an excellent tutorial. Thanks!