Hello,
Welcome to Microsoft Q&A!
Since the system considered the app as the new app due to that the app's package family name has been changed, that means common ways that storing the data will fail like roaming data and local data from this new app to the old app.
If you have a server, that will be easy to transfer data between the old app and the new app. Just uploading the data by user and download it for the new app. But if you don't have a server, you might need to use a complicated way. You might need to save the data files from the old app in some places like Document Library. Then pick the files in the new app and save them into the local folder of the New app.
Another way for this issue is that do not change the app's package family name when you try to change a new certificate. The package family name is computed from the package name and certificate's subject's hashed info, so if the certificate's subject keeps same, then the package family name will keep same as well.
Hope it helps.
Thanks.