The NAS he has already has an iTunes server
Copy all the music into the "music" folder on the DS.
Log in to the DS, go to Control Panel > iTunes (bottom row under Application Settings) > tick "Enable iTunes Service" give it a name decide if you want to give it a password, click "Re-index" and then click "OK"
Now, whenever you start iTunes on any PC on the network, you'll see the name you chose appear in the left column of iTunes under "SHARED"
You can also use the
Synology DS Audio app to control music on the NAS but I find it (the Android version) a little clunky.
Edit: Easier still, if the barrage balloon supports it, is to use
AirPlay