Perhaps this a standard procedure at Linkedin to assure SPAMmers don't leave messages? Hope not, I'd think they'd want contacts to be as fast as possible. Perhaps each "closed group" has their own 'moderator' who only visits late California time.

Therefore, you don't see any changes until the next day in Briton.
I have no idea what a "closed group" is there or anywhere else. Are there any details (FAQ?) that might explain these delays? Can you post in an "open" group and see your posts immediately?