It will drop right in. It will be very tight, but a little push should get it seated in the battery box. The posts are similar (I think the 625 uses nuts on posts instead of screws into a nut), but if you have any accessories attached to the battery they may require some small adjustment to fit. Still, not more than a 15 minute or so job.
Have you removed the snorkel from under your seat? I had mine removed when I installed the 625 so I'm not sure if there's any issue with clearance there. If there is, just unscrew it and toss it into your saddlebag. Only a few screws hold it on.
As Robert knows, the tool kit is not located under the seat on the R3T.