You were pretty close. The way to do it is registering the external SSD so that your system knows how and where to mount it. To mount a drive means to make it available to the filesystem at a specific location. The manual way only works until the next reboot, hence why you need to make an entry for this to be permanent.
Here's another thread where you can read more about how to do this:
If you want to do it through the command line, you need to edit the file at /etc/fstab (you'll need admin privileges) and add an entry that looks something like this:
UUID=C0A271C1A271BD0A /media/zenzen/TOSHIBA_EXT ntfs defaults 0 0
You can identify and obtain the relevant details about the drive you want to mount by running the blkid and lsblk commands. The two key details are the UUID and the filesystem type.
In the code snippet above, you would change the first and third fields to match that of the drive you are trying to mount. The second field is where would you like to see the files for this drive.
In your case, that should be /home/zenzen/Music — changing the username accordingly.