OK, I have a laptop with an HDD drive and I also have a SSD drive. I would like to replace the former with the latter without having to reinstall everything. What I found after a bit of research was to use a live disk + an external hard drive + gparted to copy the whole Linux partition (in two steps) and then edit fstab.
Now I guess when Linux is installed, it assesses computer's hardware and therefore adjusts some software parameters. So I'm afraid doing the above may 'fool' the OS and result in sub-optimal performance w.r.t. the SSD. I don't know if this is right.