The Disks application (gnome-disks).
If you don't already have one, create a Zorin OS BootUSB:
Boot to the Zorin OS BootUSB so none of the drives are mounted.
Start the Disks application, select the old hard drive in your computer.
At upper-right, select the '3 vertical dots' button, then select 'Create Disk Image', then select somewhere to save it that's large enough to hold the .IMG file it'll create (it'll be the same size as your old hard drive's capacity).
Once that's done, in Disks, select your new SSD drive, at upper-right select the '3 vertical dots' button, then select 'Restore Disk Image', then select the .IMG file you'd just created.
Once that's done, the new SSD has the same exact contents as your old drive.