I need to replace this button in this circuit board with a relay
The button which you have is related to a fairly common family of buttons called B3F.  A button like that would usually be Single Pole Single Throw (SPST) Normally Open (NO), as @jrtrzeciak had mentioned above.



It's good that the PCB, which you're dealing with is single-layer.  That makes it easy to trace the signals.

I think, the button is connected like this:



Furthermore, if the button is indeed NO, you don't need to remove the button.  You can connect the reeds of the relay in parallel with the button.  You'll just have 2 switches (relay and button) in parallel.