upgrading from 3.7.8 to 3.8.13.2 gold version

we are rebuilding a site and currently have gold version 3.7.8
On the Store -> Upgrades tab, it says ‘The gold version is currently activated’ and displays the key

is it possible to install the new version on the upgraded site (new hosting – same domain) and use the same license, it doesn’t seem to take a key, so need advice on how to transfer the license to new site if that is possible and upgrade.
thanks very much

http://wordpress.org/plugins/wp-e-commerce/