You want to use the left cup that comes with your new bottom bracket. Even if they are identical models and sizes, the chances are that it won't go back in to exactly the same spot and you will end up with creaking or you won't be able to tighten down the drive side enough. There are tools to help remove a stuck cup and sometimes this is easier with the BB in the frame (to use the axle to help hold the tools in place). Good penetrating oil and patience is what you want to start with. And remember to grease the new one (or some form or appropriate liquid for your frame type).