Can I download my Apple Music Subscription music on one Mac and copy to another?

I want to know if I can download my Apple Music subscription library and movies to one Mac then copy all those files to another Mac so I don't have to download all of them again and have the second Mac recognize that they are downloaded and play the file instead of streaming it over the internet . This way I won't use additional internet because I have a cap on how much I can download per month with my internet service provider. I've tried to copy the files from the Mac I downloaded everything to to another Mac and put the files in the Apple Music folder but iTunes doesn't seem to recognize that they are there and keeps streaming them.