Howdy mnobita,
To use songs that are available offline on your iPhone, you need first to be signed in to Apple Music on that iPhone. See this article - Check your Apple Music library settings.
Then you can use the steps in this article to bring that music onto your iPhone - Add music from the Apple Music catalog to your library on your iPhone, iPad, iPod touch, Mac, or PC. Specifically -
You can download songs, albums, or playlists to your device so that you can listen to them when you're not connected to the Internet.* You must download songs, albums, or playlists on each device that you want to use for offline listening.
*You can download music on up to 10 devices. These songs are accessible only during your Apple Music membership.
- In the Music app, find the item that you want to download.
- Tap the More Options icon
to the right of the song, album, or playlist name.
- Tap Download.
Songs and albums appear under My Music > Library. Playlists appear under My Music > Playlists.
Thanks for using Apple Support Communities.
Best to you.