Trying to find the right Garage Door controller

I recently moved and the garage in my new house has a (probably) very old motor in it. The previous owners supplied me with a remote for in the car which is barely working, and inside of the garage is a simple button. When pressed it’s [up] > [pause] > [down] > [pause] for each press. The button is hooked up to the motor with 2 wires, there are no other wires I can see.

What device would be the best fit for this type of situation? I was thinking of adding a Fibaro Roller Shutter, but I don’t see how I would connect it. Any ideas?

Sidenote: preferably fibaro or a wifi-solution, other protocols don’t seem to want to work in the garage.
Sidenote 2: I still want to be able to use the button inside of the garage.

One of the easiest and cheapest would perhaps be Shelly 1. It has a dry contact relay that you can connect in parallel with the existing button. It can be programmed to only close the relay for a short pulse like a button press. With a bit of luck you may also be able to power it from the motor if there is a suitable DC output. Please note that only devices with a dry contact relay must be used for this kind of application.

Doesn’t work!

You can use a Fibaro Smart Implant or a Shelly Uni.
Regarding FSI and garage door opener, please use the search function. You will find some threads about how to configure and connect the FSI.