If he received notification direct from nom sources, that does not mean that was done at the same time as submission of the slate to each SA. The noms will show up. eventually. If they don’t show by Christmas, he should contact Admissions.
Even with an LOA, all conditions fulfilled and a nom, it could still take until mid-April for an appointment to be offered. Each SA has its own method and timeline for resolving slates. They may wish to wait until all applications are in.
He is in good shape. He should continue to tend alternate plans.
“All 3 SAs” - there are 5. USCGA doesn’t use nominations. USMA, USNA, USAFA and USMMA do, so if he has LOAs to three of four, that would be spectacular. LOAs offer firm assurance of actual appointment, with or without conditions to fulfill. LOE/LOI stop short of that but encourage the candidate to complete their application so it may be considered. You probably know that, but these kinds of posts inform a wide readership.