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I would honestly just back up my files and start over with a fresh new install. I have never been successful in copying everything over, especially not if you are planning on changing the file systems. I know you mentioned that you don’t really want to do that, but that’s my 2 cents
It is possible with a little bit of work, you will have to set up grub to boot the SSD drive, there are a few how tos depending on your setup