trust – Can a client prove to a third party that they sent a message to another client in a P2P network?

Let’s say Alice sends a message to Bob in their P2P chat app asking him to complete some work. Bob is lazy, so he deletes the message off his machine, does not complete the work, and just claims that he never received the message in the first place. Their boss needs to fire someone, but is unsure who is telling the truth.

Is there a way they could improve the chat app so that Alice could prove to her boss that she sent a message, assuming that Bob is completely uncooperative?