If the bb cyl fits an 046 and the oem 046 cyl can be tweeked to fit an 044, then it would seem that the bb cyl would also work on an 044 with similar tweeks.
That said, bb kits in general have a reputation of having negligible performance gain over standard sized bore.
One reason for this, I think, is that most cylinders seem to have the transfer 'bulges' placed close to the physical limits of where they will fit into the saw chassis. almost brushing the flywheel on one side and the clutch case on the other, sometimes with a built in flat spot/depression for clearance already.
When that same externally maxed out cylinder design is bored out a couple millimeters, the transfer gets shallower by the same, decreasing the volume and also decreasing the angle the charge enters the cylinder, compromising the scavenging.
So what is gained in displacement is lost in the less efficient transfer geometry, that can't easily be regained even with porting.