By default, when you sync photos to your device via iTunes, you wont be able to delete it from your device album neither can you move the synchronized photos to your camera roll. The only way to delete the synchronized photos is to connect it to your PC and delete it via iTunes. Such a limitation imposed by Apple can be quite annoying sometimes.
A new jailbreak tweak has been released in Cydia that allows you to delete the synchronized photos from your iOS device album. Called iDeletePhotos, the tweak gives you more control over the photos synchronized via iTunes.
No setting is required for the tweak to work. Once you install iDeletePhotos, you can easily delete the synchronized photos from your device album without having to connect it to your PC and use iTunes. In addition, you can move any of the synchronized photos to your camera roll or any other album you have created on your device.
If you want to get rid of this restriction imposed by Apple on their devices then you must install iDeletePhotos. The jailbreak tweak developed by iOSDevT is available in Cydia for free and works on all iPhone, iPad and iPod running iOS 6 and later.