Assuming you speak of a Pi with openHABian (right?), you could use Amanda (part of openHABian, installable via menu). Amanda can backup/restore partitions as well as directories. You should be able to boot from SD, with SSD attached, run Amanda backup once (to backup /dev/mmcblk0 which is the internal SD card) and restore to the SSD’s device (/dev/sda or whatever fdisk -l tells you that is). Note you need to partition the SSD first.
You could also try copying that SD to SSD with a simple dd command dd if=/dev/mmcblk0 bs=4M of=/dev/sda, but you should setup Amanda anyway as it’ll take care of backing up your whole system every night.
Btw, with that in place and a little bit of tweaking, you would avoid SD corruption (well, for the most part) and don’t need to run off SSD. And if your boot disk crashes (be it SD or SSD if you still decide to move), you will be able to restore it.
