Convert an anonymous account to a permanent account

Hello!
I have implemented unauthorized access to API Gateway. When an unauthorized user signs up to my app, I want to allow them to continue their work with their new account — for example, I want to make the items the user added to their shopping cart (items in DynamoDB) before they signed up available in their new account's shopping cart.

How can I achieve this? Thanks for help!

PS. I use AmplifyJS. To get unauthorized credentials I use Auth.currentCredentials() method