Birthday video cam, which is only available on iOS-only, will appear on the profiles of a friend on his or her birthday. Tap the button and you can record your message. A series of birthday-themed frames are also available.
(A new window from LinkedIn should open for you to authorize the B&T login. If you don't see this please check behind this window, and if it is still not there check your browser settings and turn off the pop-up blocker.)