Thanks for all the inputs!!
Since I was anxious to already test it, I downloaded AOMEI partition just after my post. Went to sleep and this morning it was correctly cloned
The problem came when I replaced my old 256GB SSD and put the cloned one instead. It didn't recognize absolutely anything, and booted from the secondary HDD (which still has Windows in it, since it was the original disk in my laptop). Updated BIOS, tried several things...until I realized that the new SSD is PCIe and not SATA-III (or whatever) compatible, and that's why the laptop did not recognize it ?. The shocking thing (to me) is that the connector slots are compatible.
It is perhaps the first thing that an experienced user would look, but all those suffixes M.2, 2280, PCIe, SATA-III.... The first ones were correct, but had to be M2 SATA instead of M2 PCIe
Just ordered a new 500GB SATA-III (this time I think I did it correctly) that will arrive tomorrow....will repeat the same operation ?
Regarding the current SSD, I'll check its speed as an external drive (with the USB enclosure) and decide if I return it or use as a portable backup.
Thanks again