Take out your laptop's hdd.
Connect it to your desktop (either internally or through use of hdd caddy or usb enclosure).
Connect the ssd to your desktop too.
Clone the disk. I would suggest Acronis True Image software. When cloning if you are offered the option of copying the disk signature, select No (*).
Put the ssd in the laptop and boot, Voila!
Put the old hdd inside an usb enclosure and use it extra space for your laptop if needed.
(*) P.S. If you copy disk signature to the ssd, later if you put the hdd in an external usb enclosure and connect it to the laptop with ssd boot drive, the laptop will refuse to see the hdd as it will have the same disk signature of its boot drive.