Make sure they have an up todate address for you.
They had. Until I sent in my PPL renewal and they misread my handwriting, changed my house number from 20 to 21 and sent the whole lot to the folks across the street. Who were kind enough to give the (by then opened) envelope to me, with apologies. One e-mail and two weeks later and things were finally corrected but I can imagine that this is the stuff that causes the CAA to spend a lot of time. Other than that, issuing new EASA licenses based on current JAA licenses should just be a matter of writing the proper lines of computer code and having a fast enough printer.