I have dealt with this situation.
First make sure your opener does not have terminals on the actually opener which allow for a momentary contact (pushing a button) to open the door. If it does just hook into those terminals.
If it does not, and some do not since they only work with the rolling code buttons and openers. If your does not have the extra set of contact, take the coded button off the wall and take it apart, and look at the PCB and look for where the button to the electrical circuit is connected and solder wires to the opposite sides of the button.
I did this method before I realize my open had the extra contact, it is one thing the internet did not share that some opener has both methods, It wasn't until my open got killed during an electrical storm and I have to replace the controller I found the extra contacts and use them verse hacking the wall button.
Here is a link on doing this
http://cocoontech.com/forums/topic/2...comment=174052
This discussion show where to solder the wires on a genie garage door opener this is the open I had, the controller board in the opener also had extra contract next to the where the wall button hooks in. this can be done on other openers as well.
https://forums.indigodomo.com/viewto...p=57235&t=7364