If you’ve published an album from Lightroom and you want to be able to move it to an album set created in Backlight, you need to decouple the album from Lightroom Publisher.
In Backlight, go to Publisher and navigate to where the album you’re interested in lives. Click on the name of the album. Click on Edit. Scroll down to Advanced Settings. Under Album Management, change that to Managed by Backlight.
Go up to the Basic Settings tab. At the top is Parent. Click on the drop-down to move the album into the album set you want it in.
(if you first go to the Basic Settings tab, you’ll see that the option to change the Parent is greyed out)
One thing to watch out for if you do this is if you make any subsequent changes to the album in Lightroom. If you do, the album will be moved back to where Lightroom thinks it should be. But the management will still show Backlight and you can move it back.
I’m not sure if this is by design, but it seems to be how it works.