Assuming it satisfied design conditions for your applicable code, it could physically be welded in place with a satisfactory counterbore and taper. B16.25 would be a good starting reference.
Thanks for the info. I do have a copy of ASME B16.25-2007, but I'm unfamiliar with what you mean by counterbore and taper. As you can imagine, I'm new at this. I can see the pipe OD is the same for sch 40 & 80, which is a good start. Looking at the specifications the sch 40 would fit in the sch 80.
Best way to do this would to get a short length of 4" schedule 80 pipe, and transition (i.e. grind) one end just a little bit from .337" w.t. to schedule 40 w.t. (.237") or within 3/32" difference, such that you don't have to backweld it, while ensuring that your hoop strength calculation for the tapered of the pipe end meets the pressure requirements for your application.
"but I'm unfamiliar with what you mean by counterbore and taper"
. . . not to butt in, but he means that Sch80 will have a smaller ID than Sch40 due to its thicker wall, therefore if you simply weld the 2 ends together, there will be step-down on the ID. This is dealt with by boring a taper (bevel) on the ID of the Sch80 piece (in your case the valve) so that there is a smooth transition between IDs. B16.25 might have a recommended taper angle (or length) for connecting dissimilar IDs.
If I remember correctly, I've generally seen this in the reverse of your case, i.e., a Sch40 valve going into Sch80 piping, so the pipe gets the bevel.
