I did not know that you could transfer what essentially amounts to a non-valid license, but this is good news and will make things a lot easier.
Nevertheless, make sure you have all your ducks in a row when you send the paperwork in. If possible, get somebody with experience in these matters to take a look at the final packet and confirm everything is OK. I had the same thing and I decided to include a cover letter, detailing exactly what I wanted the CAA to do, and what sort of forms/proof I included. (And then they chose to ignore parts of that anyway...
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If applicable, make sure to include any extra, new stuff in your application as well. For instance, under EASA you now require an aerobatics rating if you want to do aerobatics. There are grandfather rights defined and if you are eligible for them, make sure you include the application and supporting paperwork in the packet. Same for banner towing and a few others. If you do not do this straight away, it's going to cost you money and frustration further down the line.
And even if you have done stuff in the past that's been expired (maybe an IMC/IR(R)), include paperwork of that as well, so that the CAA can add it to the back of your license, in the "expired ratings" section. That'll make reactivating that rating a lot easier in the future.