He may want to consider a rifle that's not too heavy to hump, that he's not afraid to shoot and can shoot accurately. My advice would be to pick up a tried an true 30-06. There's a wide selection of rifles in various weights and styles as well as a wide availability 30-06 ammunition just about everywhere you go. The .30-06 will do the job just fine on any Dear, Elk, Moose, Black, Brown and Polar Bear as well as the 30/30, .303, .308 and bow and arrow. Besides, regardless of what you might read on the internet, big Alaskan animals are NOT bullet proof. Patience and placement are the keys to whether or not the "bullet" you are using will be effective on your quarry. Folks who say that you need something labeled "magnum" or "at least a .338" are usually making an emotional judgment based on what they read on a ballistics chart or some other internet myth; not practical real world experience.
But what about self defense you say? If you're trudging through the woods and happen to stumble upon and surprise a sleeping bear, you're in trouble. Surprise one in the brush while it's eating, you're in trouble. Come between a sow and her cubs, you're in trouble. If you think that you can get off a fatal aimed shot to stop a 700 pound bear that's just as surprised as you are and bent on defending itself with everything God gave it to do the job, good luck, regardless of what kind of cannon you're carrying.
Situational awareness and using the best weapon available to you, your mind, will provide you with more security than a .375 H&H. Do yourself a favor, pack an electric fence in bear country, if you're that concerned with it; carry a can of bear spray, just smart in bear country; and whether it's a .308 or a 30/30, hump a rifle that you're not afraid to shoot and can shoot accurately. Be patient, the shot will present itself. If not, at least you have yourself another good memory.
Best wishes.