Will a 2007+ Sportster Transmission Fit a 2005 883?

Hi everyone,
I’ve got a problem with my 2005 Sportster 883. I need to replace the entire transmission/gearbox, but I’m having trouble finding a complete 2005 gearbox.
Does anyone know if a transmission from a 2007–2022 Sportster will fit a 2004–2005 model?
I know the early bikes use straight-cut gears and the later ones use helical gears, so I’m not sure if the complete assembly is interchangeable or if there are other differences in the cases, shafts, or bearings that would prevent the swap.
Has anyone done this swap, or know if it’s possible? Thanks!