Need help finding part to fit Briggs & Stratton engine 104M020198F1

Hello,
I purchased a new Briggs and Stratton engine 104M020198F1 725 EXI Series  for my lawnmower and I am having such a hard time finding the part that has the pulley and hub that will fit so I can attach the blade and actually use the mower.
I have since learned that even though the original mower used the same exact model number Briggs and Stratton engine, each manufacturer is a little bit different and the piece from the original mower doesn't fit.  I've bought (and returned) what Amazon said "others who have purchased this item also purchase these" and a part that looked similar with very close measurements but there's a notch on the shaft that is just not matching up to what I've been able to find.
I tried the Briggs and Stratton Online Store, and they could just send me the manual for the engine, and wouldn't be able to tell me any information about parts for it. I tried a couple local places, but they wouldn't listen to me. One kept telling me I had to go back to the original manufacturer and the other told me to return the new engine and bring them the old one to fix. (the old engine was not able to be repaired and I don't have it anymore). 
I stupidly thought it would be easy to just buy a new engine, attach it to the old mower and move on with my day, but that has not been the case. 
I've attached photos but if anyone could please even point me in the right direction I'd be so grateful.
Thank you for your time.