The good news is that your JAA Licence
is already deemed to be an EASA Licence. You only need to visit your local ATO/RTF,(Flying School) and renew/revalidate your SEP Class Rating.
Once you have done that, you can apply for your Licence to be re-issued as an lifetime EASA PPL anytime before it's 5 year expiry date. The Flying School will have done lots of these recently and will help you with the forms.
You can update your address at the same time.
MJ