MDU,

Let's concoct a plan for H! Now is a good time to do so. I recall a wonderful moment when an XGF sent me a tin can of gourmet popcorn (three flavors) along with a note wishing me well prior to sitting for my MBA entrance exam.

Now would be a good time for you to do something like this for H. You could say something along the lines of:

H, congrats on your promotion. I believe in you! You got this and I am so proud of you! Love, MDU

You don't want to order a 3-gallon tin where H will share it with other co-workers. Go small so H can have it all to himself. After all, this is all about him. You're showing support for H in his career and I think this is a wonderful way to show it without being all mushy.