Let’s hope that is not the case here , it might as well be that the new drive is not recognized by the BIOS ore bad connection cables, or something like that. There is also a sdc , that I was wondering about.
AME MAJ:MIN RM SIZE RO TYPE MOUNTPOINTS
sda 8:0 0 238,5G 0 disk
├─sda1 8:1 0 1G 0 part /efi
└─sda2 8:2 0 237,5G 0 part /
sdb 8:16 0 37,3G 0 disk
└─sdb1 8:17 0 37,3G 0 part
sdc 8:32 1 0B 0 disk
If I am to believe his word (500 GB), then it is a possibility.
How much did you expect? What was your assumption about the size of this SSD?
The parted command is not lying. This is it. There is no more space. Even if there would be unformatted space on that device, parted would show it.
That is not what parted is showing. It shows an existing ext4 partition. So this SSD was clearly formatted with a Linux PC.
Something is odd here.
Maybe it does. We are living in the post-truth world so I am not surprised 
Thanks a lot for your answers.
Unfortunately I bought a small sized SSD. It is what it is. There is only a 37 gig partition, because the drive ain’t more space. My mistake. But on the other hand I found my SSD and could use it.
But, but… what about..
But how come that there is an ext4 partition on that SSD? If the SSD is new it should not be there.
Found a review of the SSD that is from 2010.
If I was the TS I wouldn´t want to put any important data on this SSD.