Just guessing, having never used one, the only thing missing is a threaded rod that holds those squared off round plates. The way the hole is drilled in them, they can tilt at an angle to drop down through a cylinder with sleeve, then fall flat to engage the bottom of the sleeve. The cylinder is placed on the base, the bolt somehow suspended the from the cross bar, then jacked up. The cylinder would have to be held down somehow.
That looks shop made. These are guys are spot on. There would be a rod between the puller and the adapter to pull the sleeve. Normally with a pivot at the adapter end.
That larger triangle shaped plate is used to install a sleeve. It would go across the bottom of the block. I suspect the other large plate is for the top when installing a sleeve.