Not a new sprocket

Today I tried to fit a 14 tooth sprocket. Previously a 'local' Beta dealer told me the official sporckets were on a long back order and so I had acquired one that supposedly fits a DR350. But the splines were of the wrong size and pitch. I suppose the issues are:

• Was the one I had really a DR350 fitment?
• Is the Beta 350 output shaft unique?
• Does anyone have the Beta Alp part?

I adjusted the tyre pressures too, they still had a lot of air which suggests that I'd not nipped the tubes.