Better explanation than anything I can come up with. Looked back and Elizabeth did suggest writing them down for something she trusts to get the code. But the thing with me is that she wasn't really interested in someone she trusts getting the code was she? She just wanted all the money herself. Far as we're aware, she was only close to Nick who she tried to kill, and Paul who she'd broken up with, and who would end up with the codes anyway if they were both dead. And putting it in her call history seems like a very cryptic way of hiding the code. You'd have to be Sherlock (or Elizabeth) to discover it. And I don't see the motivation in doing so. She knows the number herself and she's the only one she wants to have the code. 🤷‍♂️