Importing Song that is Not Available

Hello, I recently accidentally deleted a playlist from my iPhone. I was able to manually recover it by opening iTunes on my PC before connecting to the internet, so I could see the playlist before iTunes refreshed and noticed that it was deleted.

However, when adding the songs manually to a new playlist on my iPhone (using the list from my PC), I ran into a song that is no longer available on Apple Music.

After searching for this song, I thought the best way to recover it to my library would be to open an old iTunes library file on my PC. I opened an old .itl file and I can see the old playlist with the song that is no longer available, but if I reconnect my PC to the internet, the library updates to my current library.

How can I use that old library .itl file to recover the one song that is no longer available on Apple Music? Is there a way to manually move it to my iPhone? For reference, when I open the Song Info from that old iTunes library, under File, it says the iCloud status of the song is Apple Music, and the location is iCloud.