I don't believe they transfer to each other. Maybe in a brand new lifter, more pressing strength may help a jerk, but probably just because they don't know how to jerk properly. I've gone long stretches of just doing jerks and adding a lot of weight to them, and when I go back to pressing, my numbers have barely improved. Same thing vice versa, pressing for long periods does not help my jerk. It's hard to "prove" either way though, with most lifters in the beginner and intermediate stage, improving the squat, clean, and snatch may improve the jerk, and credit may erroneously be given to pressing.
There are other things at play here though, pressing and upper back exercises can add size to your upper torso and shoulders, which may assist in holding/stabilizing a larger load, better enabling you to jerk it (hehe), but credit should not be given purely to pressing strength.
If you're interested in beating your friends at the jerk I'd suggest you keep improving your squat, oly lifts if you do them, and add size to your shoulders/back. Then, you are correct, you will have the potential to jerk more weight when the time comes.