An iOS device can only be synched with one iTunes library at a time.
If the phone was previously synched with other iTunes library on another computer, it will tell you so when you plug it in to your iTunes. It will then ask if you want to erase the music and synch your own. So you will not be able to transfer the music to your library.
If it has not been synched you might be able to meld the songs on your uncle's phone with your library.
There might be more answers here:
Transfer content from an iPhone, iPad, or iPod touch to a new device - Apple Support