To transfer mobile app purchases to your library on your computer such as iTunes, connect your mobile device to the computer and click the File menu option once the icon for your device to appears. Select the Devices link, and choose the option to transfer your purchase to your device. You can also move your apps using the Syncios software application.
To move your apps to your library using Syncios, select the Apps link under the My Device tab, and pick the option to back up information from iDevices to PC. Select installed apps from your device, and hold the Ctrl/Shift key down. This action allows you to choose different apps. Select the Backup button, and search for a location on your computer to back up or transfer your apps. Backup these apps from your mobile device to your computer.
As of 2015, Syncios is free and allows you the option to transfer many items from your mobile device to your PC and iTunes library including your apps, contacts and messages. You can also transfer other media purchases to your library including apps, music and videos. You have to install iTunes to use the Syncios software.
If you decide to transfer your apps using your mobile device, make sure you authorize your computer with your Apple ID. You can also use the iCloud to transfer apps to your library by signing in to iCloud with your Apple ID. Check to see if the apps are transferable and available to download again. If the app is not available in the iTunes store, you may not have access to re-download it.