iCloud doesn't back up your local music (imagine the storage required if it does).
This is going to take a bit of work, and assuming your dad has access to a computer, and somebody can access his computer, and that you have a cloud storage with ample enough room for your dad's music library.
1. Find the iTunes library folder on you dad's original computer.
2. Upload the whole folder into a cloud storage of your choice.
3. Download the folder into a computer that he can access now, retaining all the folder structure.
4. Then you can run iTunes on the computer. Basically you're duplicating his iTunes library.
On your PC, use the iTunes backup feature to move your library to a new computer.
support.apple.com
Or, for temporary solution, just have your dad subscribe to a trial of Apple music. At least he can listen to some music in the meantime until he returns to his home and resync his music library.