He needs to fill in a V62 form, available from the Post Office or from DVLA's website.
Does he have the green New Keeper Supplement? If so, he can send that in with the V62 to avoid the charge for a duplicate logbook, otherwise it costs �25.
Now MOTs are computerised, you can obtain a duplicate MOT certificate from any testing station - it doesn't have to be the one which originally did the test. However, they will probably require sight of the logbook to do this. Duplicate MOTs cost a maximum of �10.
Until he gets the logbook through (which can take up to six weeks), he won't be able to tax the vehicle, so he will need to arrange to park it up off the road from the day the tax expires until he is able to retax it.
He should also complete a V890 SORN Declaration in the meantime, to declare the vehicle off the road while it has no tax.