Smartphones

You can capture music streams with Audials. http://audials.com/en/how_to_record_stream_capture_music_videos_movies_from/apple_itunes.html

Best Way for copying, downloading & recording Music from Apple Music™ and Apple Radio with Audials
Step 1: Start Audials Tunebite, Tab “Streaming - Save Music”
Step 2: Click “Apple Music“ tile. Play back Apple Music iTunes Streaming in Browser
Step 3: Music will be automatically saved as file (e.g. MP3/AAC)
The Apple iTunes™ video streaming can be recorded and saved in the video file formats MP4, WMV, AVI, 3GP or others. The Audials Windows software tool will tag the file of the movie or the episode of a TV series afterwards.

Apple Music is all about streaming. You pay a flat fee to unlock access to Apple Music's entire catalogue, but you don't actually own the music you listen to.
To solve the above problems well, Macsome iTunes Music Converter is helpful and useful, which uses high recording and encoding to MP3 / AAC technology to convert these DRM Music files to MP3 formats, and then you can enjoy these files on any MP3 player devices as you like. (http://macsome.com/itunes-converter-mac/apple-music-converter.html)
Step 1. Free download the latest version of Apple Music Converter for Mac OS X, install and run it.
Step 2. Click the Add button to load your Apple Music files.
Choose the Music library in the drop-down list, and then choose the Apple Music files you want to convert.
Step 3. Click iTunes Converter Menu – Preferences – Advanced to set the output audio format, here we use the default one: Same as source.
Step 4. Click "Convert" button to start the converting.

Anything you have in Apple Music you can easily move to iTunes. Click the ... next to the track and select "Show in iTUnes Store." Then you'll own the tune even after your Apple Music trial is over.

Naturally, you'll have to shell out the buck or whatever it is, but it's the only fully legal way to keep the song on your device.

Try out MusConv to convert your music and playlists into different music platforms. It's easy-to-use and I'd highly recommend it.

Try MusConv.com tool for Apple music

To help you record music on your Mac PC with ease, here are the top 5 Apple music recording software programs that you can use.

1. iMusic
2. Apowersoft Mac Audio Recorder
3. Audacity Audio Recorder for Mac
4. Apple GarageBand
5. Onde Audio Recorder for Mac

If you are an apple user and love music then this question will definitely come to your mind and the answer is yes, there are some free software that help you to record the music from Apple Music. Here is the list of some software used to download music from apple music.
1. Apowersoft Mac Audio Recorder
2. Audacity Audio Recorder for Mac
3. Apple GarageBand
4. Onde Audio Recorder for Mac

if the site allows downloading, you do not need any software, just right click it.

Top 5 Best Apple Music Recorder Software

1. iMusic
2. Apowersoft Mac Audio Recorder
3. Audacity Audio Recorder for Mac
4. Apple GarageBand
5. Onde Audio Recorder for Mac