Just to clarify, that SSD you mentioned looks like a USB 3.1 SSD yeah?
If so, then the adapter linked is no good since that is USB 2.0
You'll need a USB header adapter that is for 3.0/3.1
While it is stated as USB 2.0 compatible in the specs list, that just means you can use it through 2.0, but the speeds will be significantly slower than the potential of the drive.
Alternatively, if you are certain that you won't need the external drive at all to be external again, then you could break open the enclosure and just plug it directly in like normal.
The SSD within will either be a 2.5" model, or it will be an M.2, and if it's an M.2 you'll need to ensure that you have an M.2 slot on your motherboard.
Judging by the specs with the width being only 49.5mm (which is about 1.9") it might be an M.2 SSD inside the enclosure.
Use a 3.0 header not a 2.0 header if going with the USB cable adapter option.
If you motherboard happens to have a Type C port on the back, you can instead plug a double ended Type C cable into that port, then pop out one of the lower slots for GPU and run the cable into the system, then plug that into the SSD.