There's lots of good reasons Not to donate to a museum.
Consider that your rifle is a very nice one, is one of only two known signed by this maker, and is worth about $3500 / $5000, and maybe a good bit more to the right collector.
When you donate to a museum, that generally means the gun legally belongs to them to do as they please with it. They can chose to display it, or store it in the back room. They can also sell it, trade it, give it away or throw it away if they decide it doesn't fit their mission. Not to mention the number of guns that have been stolen from museums, or walked out the back door.
I'm not saying that will happen at the Huntington Museum, but if decide you donate it to them, first ask them if they will keep and display the rifle for ever, for all to see.
John