I struggle to see how both statements can be true as they are directly contradictory. Either Letby called Jayaram as he said in this email, or she didn't as he said in court. How can she both have called him and not called him?
And no, this is not what the Thirlwall enquiry is for. That enquiry is proceeding on the assumption that Letby is guilty and will not consider any evidence to the contrary. The question they are looking at is how she managed to get away with it for so long. Other explanations for the deaths such as the babies all dying of natural causes, as many medical experts are saying, are not being considered at all. And the enquiry isn't looking at the evidence of her guilt at all. Conflicts between what Jayaram said in court and what he said in emails won't even be mentioned.