So it looks like someone reversed the leadscrew and drilled the fixed jaw so that the handle end came out the "back" of the vise.
If that's the case then yes you could put it back the way it originally was but you might need to make or buy a new longer piece of acme screw stock.
ps Roton stock is fairly reasonable www.roton.com
On my vise as you saw on the drawing it just extends out of the bushing in your first picture. the end that extends out has a pin that extends from the shaft on both sides to keep it from going back in but the vise action is from the back jaw and the nut that is on the other end of your shaft that is still on your vise. On the end that of the shaft that is missing on your vise it has a 3/8" square end. You should be able to make a new shaft from a ACME allthread without much problem.