Will a locking diff gearbox fit any car?
 

I just ordered a used transmission with the locking diff function and I'm not sure if my car has that option. My question is, will this gearbox my car although mine might not have the option?

Sometimes you will need the matching torque tube, depends on what model you have and what model you are trying to put in. Tell us which car you have and the trans ID stamped into the bottom of each of the transmissions.

BTW in general ALL used transmissions with a LSD will have the friction plates worn out and require rebuilding, so if you can it might be easier to remove it, rebuild, and swap into the transmission you have now.