If the applications are downloaded via iTunes, they will be automatically transfered to the iPhone during synchronization. Otherwise, the apps downloaded via iPhone will be copied and backed up to the iTunes during synchronization. So to transfer the apps to the iPhone, just connect the phone to the iTunes and sync.
Click on iphone on the side bar, then apps up the top, then sync apps.
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In itunes, select file - transfer purchases from "name of iphone". That should work.
use copytrans is easier, drag and drop
In order to see your downloaded apps from your iPhone, iPod, and iPad, you need to authorize that on the computer first. Go to iTunes/Preferences/General. Is there a check mark next to Applications in the Show section? Checking this will show the apps folder under the library menu. Once that is done, right click on your device icon '(your name) iPhone' and click transfer purchases. All your apps should start downloading.
Actually, there are several ways to transfer iPhone music to iTunes. The best way I know is to use a third-party app such as this one (copytrans.net) if you run a PC or this one (xtremsoft.com) if you are on Mac. You will find further info on this interesting blog: http://ipodtocomputer.blogspot.com
if it is an iPhone, iPhone 3G or 3GS