Isn't it somehow the manager's job to make sure that what is good for Anne is aligned with what is good for the company?

If Anne makes a great documentation and teaches Beth everything she knows, it may save the company a lot of money. How about giving a part of that money to Anne as a reward for being helpful?

Or is it just Anne's moral obligation to ignore her own utility function for the benefit of the company? If so, then in addition to making the documentation and teaching Beth, she should also ask the company to give her as small salary as legally possible. (She could also sell her kidney, and donate the money to the company. Perhaps do the same thing with the second kidney on the day that Beth is ready to replace her.)

Also, it is the manager's job to decide whether it benefits company more if Anne works on making herself replaceable, or if she fully concentrates on doing what she does best. Maybe making Anne spend a part of her time writing and maintaining the documentation would cost company $500 per month; the risk of losing Anne in any specific month is 2%; and the cost of replacing her without documentation is $10,000. Then the rational choice is not to let her work on the documentation. Anne does not know all the relevant numbers.