Dear Ismael,
The main reason for sending letter to the client, is to record that the client action (event) is subject to additional time and/or cost. At this stage, we might not have full details about the event consequences. For example, if your contract is under FIDIC, you should notify the client within 28 days from the event date that there are time/cost impact. Furthermore, some events sources are contractually weak, like comments on shop drawings, so we want to make them stronger by issuing a letter to explain the case. Finally, later on in this course, where we will create the narrative, we need this supporting letter to reinforce our status that each event by the client was recorded by a supporting letter from our side.
Best regards,
Hany Ismael