I congratulate him/her on the achievement (because I also know what work went into this!) and remind the author to tell us on LinkedIn.
I always remind that this should be posted on LinkedIn in 2 places: 1) as an update and 2) in the Publication section.
This is not ego-centered. It’s practical. Why?
You post as an update on your Home Page so your connections see it in real-time. Then tomorrow, the posting will be far lower as new updates come in and overlay on top of it.
You post in your Publications section on your personal profile page so it is memorialized for the long-haul and visible to anyone who sees your personal page.
Don’t forget to post it in both places.
Grab the URL, (or shorten it on bit.ly if necessary), add a brief description of what the reader is about to see and you are all set.
No need to do this if it’s a long-form Post on LinkedIn, since it follows you as part of your profile.
But if it’s a video, well, see my earlier postings on that topic….