Yes, the sleeve is an integral part of the bag when purchased. This is referred to as a 'Trolley Strap' which means it slips over the handle on a roller suitcase. Some are just wide enough to fit over a handle. This one was the full width of the bag which meant the frame didn't have to be trimmed as much. It probably also is more stable than something that provides a more narrow width. There was a zipper in the lower portion that I had to cut back and remove the pull in order to open up the whole width through the strap.

ShortLegCyclist, your suggestion is essentially what I did, although I had to cut the frame width down a bit. Because the frame is covered by the bag, I think it has a cleaner look than exposed attachments. I bought an S-bag frame, that was the $33 expense, and modified it to fit.