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Once the barrel is removed from the proximity of the weapon it no longer falls under the National Firearms Act. But unless there was a real compelling reason not too, I would destroy the barrel.

From a strictly legal point of view an attorney working for the estate can contact BATFE and ascertain if the weapon was registered by the decedent. If it was, it can be transferred tax free via a Form 5 to the legal heir as long as they are not a prohibited person and it is legal for them to have possession within the jurisdiction.

It is a SBS, and unless it is worth a great deal of money, it is just not worth the effort.

You can turn it over to a police department, a museum (if it will take it), or destroy it. Those are the practical options. Don't get sideways with something that is basically worthless. If it was a 1928 Overstamp Thompson in mint condition or a BAR, it would be worth the effort, a SBS, not so much.