Yes. The apps will work on any iPhone (or iPod Touch) that's synced with any computer that's authorized on your iTunes account. That is to say that not only will they work on another iPhone (or Touch) that's synced to the computer your current iPhone is synced to, but if you have another computer/s (up to 5) you can load the apps on those computers and sync them to iPhones (& Touches) as long as those computer(s) are authorized on your iTunes account. The best part is that not only will it work, but it's legal on those (up to 5) computers, and iTunes (the iTunes Music Store, really) won't let you authorize more than 5 computers on your account.