[RPKESQ]

I do not recommend welding. You will never match the temper and crystalline structure of the surrounding metal. And barrels on shotguns are typically made of much more ductile steel than rifles or handguns (some manufactures have experimented with higher strength steel for shotguns and have had serious problems). The evenness of flexibility and ductility is important as you do not want to set up any stress points. Stress points will lead to failure.

Shotgun barrels with this type of damage can only pass proof by utilizing the following methods:

Sleeving (1) - by replacing the barrels and inserting them into the breech section.

Sleeving (2) - By replacing the breech section and inserting the original barrels.

New Barrels - Complete new barrels.

In this case I would consider the welding as a cosmetic repair only and permanently plug the barrels.

If someone was willing to undergo the cost of a working repair, I would go looking for a good used set of barrels first and consider sleeving (1 or 2 depending where the damage is located) as the second choice.