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How do automatically save music to SD card?
Transferring media files to a memory card
Make sure that your device has a memory card.
Open the Home screen and tap.
Find and tap Settings> Storage and memory> Transfer data to SD card.
Mark the files you want to transfer the memory card.
Tap Move.
Hi @AlexandrosGinn, welcome to our forum!
Do you want to save downloaded music directly to the SD card in your phone, or do you want to transfer it from a computer to your SD card?
If you are using a music service that allows you to have offline lists, there may be a setting in the application to save these offline lists directly to your SD card. This is depending on if the developer of application has added this feature in their app.
I see that @67Kiisseli have given you great instructions on how to move data from your internal storage to your SD card! Thanks a lot for helping out! 
Let me know how you transfer the music to your phone and I will do my best to assist you further! 