He can get the letter from VFS or the Embassy will post one, see here;
Transferring your Thai visa after renewing your British passport
This service is available in person at VFS Bangkok or online and is free of charge.
The Immigration Bureau in Thailand may require a letter from the British Embassy in order for you to transfer your visa from your old to your new British passport.
You will be given a template visa transfer letter from VFS Bangkok when you collect your new passport. You can also request a letter in person by visiting their offices, from 8:30am to 3pm, Monday to Friday, at 8th Floor, VFS, The Trendy Building, Sukhumvit Soi 13, Klongtoey-Nua, Watthana, Bangkok 10110. Alternatively, apply online for a letter to be sent to you. To request the online service send a message via our online contact form, giving the reason for your request along with your name and address in Thailand.