If I was doing this, I would tap the audio leads to the speaker, leading them to a 428-13 tremolo control box; the output of the box then would go to a 6-pin jack on a bracket from tonewheelgeneral.com. Then you figure out what kind of tremolo switch you want, buy it, and install it. You also need to find a source for "switched power" for the jack, try looking underneath the metal box cover.
Finally, if I wanted to be able to switch between using the speaker and the Leslie, I would put in a 3M box or its equivalent (they are very simple to build) and a main/echo/ensemble switch. I DIYd my last M/E/E switch to be a sliding switch on the back of the organ since I don't need to change that mid-song.
Another way to do this is to use a 26-1 kit, modified to use a 428-13 box to do the tremolo switching. That's great if you have the 26-1 kit and need M/E/E switching but otherwise is a waste of money IMO.
Of course, there's probably an official way to do this described in the first couple of pages of the Leslie 122 owner's manual, but I forget what it says about the M3.