Welcome to the Community,
what should work is to do an OVA export/import from the Embedded Host Client, i.e. export the VM, remove it from the host's inventory, and then import the VM to the SSD. What you may want to do before powering on the imported VM, is to temporarily remove the imported VM from the inventory, copy the VM's .vmx, and .vmxf files from the "old" folder on the HDD to the "new" folder on the SSD, and then add the VM to the inventory again. After powering on the VM for the first time, answer the question that will pop up with "I moved it". This way the vCenter VM will keep its UUID and MAC address.
Note that the above assumes that the vCenter Server VM doesn't have any active snapshots!
André