Please be well noted that Apple Music are encoded in M4P format, which is not compatible with MP3 player, unless you have converted them to MP3 format.
To achieve this, you need to use Apple Audio Converter to convert Apple Music M4P to MP3, and then you can freely transfer Apple Music to MP3 player for playback without limitation.
For the detailed tutorail, you can refer to this source page: How to Convert Apple Music to MP3
