Mate/George is of course spot-on. Here’s the scoop from this page: https://www.propellerheads.se/support_area/index.cfm?fuseaction=get_article&article=product_r egistration_faq -
I've lost my license number. What do I do?
So, you've lost your license number? Here's what you can do to get a replacement number from our distributor or us:
§ Have you registered the license number to your user account? All your registered license numbers can be found in the "My registered products" section of your user account.
§ Do you have parts of the license number? Send it to us.
§ Dig out your receipt. If you've bought it in a store, contact them or contact the local distributor. We are not responsible for any sales that take place in stores.
§ Do you have an old song-file that you've made in Reason? We can extract the license number from that song. Please send it to us in a zip.
§ Send us pictures that verify your possession of the software.
Send this to Customer Care.
I had a similar situation three years ago and wrote Customer Care; give them your old email address as well if you can but the pic described should do. They had me up and running in three days.