The genuine PO rubber strap with 20mm lug width fits on the 4th generation PO rep. I have mine almost permanently on it.
I've also tried it on the double ridged genuine seamaster strap, but wasn't happy with it.
The genuine straps are made of a different rubber composition that doesnt seem to pick up dust as easily. Conversely the Doxa rubber strap seems to pick up dust, but that could be because of the grooves on it. On second look, I think it is the grooves, the back doesn't have any dust.
The genuine PO strap with 22mm lug width also fits the "Ultimate" PO 45.5mm. Silix have a rep 22mm rubber strap out, but too late for me
The genuine straps seem to have much stronger/solid ends that attach to the case which seems to prevent it flexing away from the watch and leaving it snugly fit to the case.