Like everything using wireless tech there has to be a matching ( digitally coded ) receiver in order to use the wireless button. I doubt there is a function within the lamp that allows the user to "boot sync" the button but I might be wrong about that.
Likely if you break your button you will need the serial number of the lamp to order a replacement button that will sync with your lamp head.
I bought both the MJ-906 and the MJ 902.
I tried using the wireless button from the 906 on the 902 and it paired and
works. The same was possible with the wireless remote from the 902, it
paired with the 906 and is working too.
So the wireless buttons are pairable with any remote from the 900-series. At
least it worked with the 902 and the 906. I also paired the remotes back to their
original lights they came with, and they are good to go.
This means there is no serial matching on these remotes, and they are not
binded for life to the light they came with.