Your best bet is to clone the hard drive to your new SSD Here is a video that shows you how.
Cloning a disk using Macrium Reflect 7 - YouTube
Follow directions you'll have no issues and be up and running on your new SSD in about 20 minutes
With Cloning, you won't have any issues keeping your Pro version you will be automatically Activated because you new SSD is a clone of your hard drive Windows won't even notice the difference
Reading your 2nd post you're active for Pro on the Dell so that won't activate on the HP the Windows is only good for one computer the activation servers has the imprint of the Dell and the HP so they will not be transferable
MR has a feature for restoring an Image to different Hardware, this seldom goes will on notebooks, even it did it probably would deactivate and request a new product ID
All that said, you Have MR make good images of Both computers and give it a try if it fails you can go back with the images you created before attempting.
Really you should do the right thing and purchase a new Pro upgrade its only $99
You would have to deal with Windows Store as to perhaps moving your Pro upgrade it may be possible I have never tried