A and B pretend they never knew anything about it. Malorganisation, a word for this massive falling between the cracks, sums up most large firms.
Symptoms are a chronic lack of communication, endless paperwork and e-mails, and a boss who hides behind his secretary. The solution is to do the unthinkable: sit down and have a conversation. Introduce head of Department A to head of Department B and suggest they go to lunch. Ban e-mails for a day and suggest employees relearn how to use the phone instead - works miracles.