JackE said:

You must first initialize the SSD using a 2.5" USB-to-HDD/SSD cable (less than $10 from Amazon) using ControlPanel's disk manager. Then you have the option of cloning or migrating the system on the old HDD to the new SSD through the same USB port. Or you can replace the old HDD with the new initialized SSD and install a new version of Windows on it with a USB installation stick.  Jack E/NJ

Same problem here (same pc model and SSD). I am not sure what initialize means but before I put the new SSD I made an exact copy (with that cable) of the current HDD into the SSD using Macrium Reflect. When the laptop is on, the SSD gets detected through USB, but if I go to BIOS (which I got updated to the last version) it doesn't show up. So when I put the SSD inside it doesn't show up either.
My only guess now is that is a Kingston problem. I might change it with a WD since the original HDD belongs to that firm..

Anyone has better guess?

JackE said:

The SSD will not show up as a bootable drive thru the USB port. However, once connected inside the machine the SSD must show up on the BIOS Information tab or it has no chance of booting or showing up in the BIOS Boot tab. If you used Macrium's auto migration function to copy the partitions from a bigger HDD to a smaller SSD, this often doesn't do the job as well as the cloning function in which you first manually shrink the system partition on the bigger HDD so it will fit on the smaller SSD with the cloning function. Jack E/NJ   

I made it. Bought a second SSD (WD brand, which is the same of the laptop HDD) and followed your instruction. However, since the very beginning this SSD was detected internally both in the BIOS information and boot. The Kingston didn't, so I am prone to believe that it still might be an incompatibility matter. In any case the laptop works and I couldn't be more satisfied.
Thank you for your time and patience.