You can't do anything about getting a UK licence until you are there because you'll need to send off your passport and visa to the DVLA when you apply for your provisional UK licence... So you just need to wait until you have moved to start the process.
Once you have sent off for and received a provisional licence, you'll need to go through all the UK driving tests - theory and practical- to get a full licence. It's a good idea to take some driving lessons too, to learn how to pass the test.
You'll have to check the US Embassy website to see whether he needs to have a particular amount of time left on his passport to travel to the US (some countries require 6 months left on the passport). However if it expires in June anyway, he might as well renew now, before the summer rush, since you can apply to renew a UK passport a few months before it expires anyway.
Sent from my iPhone using Tapatalk