I bough a wireless doorbell, this is the remote pushbutton. A thread.

I disassembled the remote pushbutton to check whether the button had accessible solder points or not. It had!

In the wall outside is still the original doorbell pushbutton. The wire has been cut and the hole covered. It does nothing but the button still works

So I connected the old button in parallel with the new one, dead simple.

And now I have a working wireless doorbell with the exact same look and feel as the old one. Success!! (End of thread)