The same is true if he donates the shares directly without going through an LLC.
If any of the shares the LLC holds are liquidated by the LLC or granted to for-profits, situations where the "other reasons to create the LLC" are in effect, capital gains tax WILL be owed.
The LLC is as if he held the shares personally, when it comes to capital gains.
The estate situation is very different, not cut and dry, and that's what is being discussed in this article.