Instead of a formal "appraisal," he might be able to get by with estimates of value from a couple of gunshops.
There are several in the Springfield area that could probably provide the service:
Gilberts on Route 1 in Woodbridge.
Shooter's Paradise in the Marumsco Plaza in Woodbridge.
Blue Ridge Arsenal in Chantilly.
They, likely, would just look in the Blue Book of Gun Values as Jim has indicated. Unless the gun is ultra rare, valuation will likely only be a few hundred to a few thousand dollars.
As for the handgun laws, tell your brother to make sure the gun is unloaded, and then wrap it in a clean, dry cloth, put it in a cardboard box, tape the box shut, and put it in the trunk of his car. If he can't put it in the trunk of his car, then it must be in the area farthest away from the driver.
If he follows those steps, there should be no problems for him.
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Beware the man with the S&W .357 Mag.
Chances are he knows how to use it.