If you just have one or two to do, this is the easiest way. If you have many to do, the Design Assistant utility is more efficient. Or, if you are using Vault, there is a Copy Design tool that will make life easier for you.
I would modify your technique just a little, though. Simply copy partA and drawingA to partB and drawingB. Then open drawingB and Replace Model Reference.
You don't say which version of Inventor you are using, though. The Replace Model Reference tool is only in the last several versions. Before that, the same procedure applies, but you would also need to temporarily change the name of partA so that upon opening drawingB Inventor would ask you to find partA, and you choose PartB.