Good luck with this.
The FAA letter is valid for a maximum of 6 months, or the verifying authority's duration. The GCAA were previously only issuing letters valid for 90 days…
…which makes great fun for all, with the FAA's quoted 45-60 day processing time for these letters, and potentially another 4 weeks for TSA approval. Not to mention the cancellation policy for the Part 142 school…
You may find it easier to add the B777 to an EASA license (if that’s what you previously held), then get a full 6-month verification letter to take to the FAA. PM for more details?