It looks like your one has a different footprint to the SJ2-35464A-SMT-TR you may not be able to solder it onto the board.
The mapping of pins to contacts on the plug also seems to be different so these ones won't work I'm afraid.
Thanks Alex for your helpful reply!
Note that while the pins don't match, if you're willing to get a bit creative you can make any TSSR jack work - you just need to solder three wires from the Tip, Ring 2, and sleeve pins on the jack to one of the L signal, plug detect and ground pads respectively on the board and you should be good to go. I did this with a TRRS breakout board from Amazon, a number of resellers have them (sparkfun, adafruit), glued the breakout board to the side of the battery case, fastened down the wires and it works a treat.
Thanks Seth! In the end I got a colleague to help and he did exactly that, though he glued it to the top surface rather than the side. A good solution and works fine :-)