OctoPi hardware upgrade

I have latest OctoPi release running on RaspBerry Pi B , all configured and well.
Bought Raspberry Pi 3 B+

Can I just move the SD card and boot as usual, or should I do some hardware configuration commands, or... just backup & start fresh ?

The fastest, easiest seems to be to move the SD card, unless there are some reason not to do that.

As long as the kernel is new enough, yeah. Put a monitor on it and you'll see if there are any errors.

It would be prudent to make a copy of the image first (ApplePi-Baker, for example). Then after the move: sudo apt-get update && sudo apt-get -y upgrade to bring the firmware up-to-date.