SOLUSfiddler If you are able to mount the new SSD, then couldn't you just do what @Justin proposed in a terminal (/dev/sdb1 should not yet be mounted), i.e.:
sudo mkdir /my_new_drive
sudo mount /dev/sdb1 /my_new_drive
sudo chown -R $(whoami):$(whoami) /my_new_drive
Then, one cannot view properties of a drive in the file manager, just of the directory where it is mounted. If you mount the drive by clicking on it in the file manager (without having changed the mount point) it will be mounted to /run/media/[your user name]/[partition label] (or the UUID, if you haven't labeled the partition). Thus, you could right-click on this directory, open the properties and adjust the permissions as @Bruce-McL proposed.
