Add music files from my computer to an iPhone I need to put some music files on somebody's iPhone. 
How can I do that without erasing the content of his iPhone ?
You can only sync media from one iTunes library with the iPhone at the same time.
This applies even if you have activated "Manually manage music and videos".

If you see a message that the device is synced with another library, iTunes can't sync the music without first erasing and replacing all iTunes content on the device.

Source: https://support.apple.com/en-us/HT201593