The new IDE should actually know the list of those packages.
All you need to do is to go once to the menu: Tools > Build Lazarus with profile ....
And then when the IDE restarts they should be all there.
If rebuilding doesn't help, then you're probably using a different configuration directory (if you checked the "Secondary installation" checkbox during installation).
Then you can use the "Import" and "Export" buttons in the "Install/Uninstall Packages" window. They will allow you to save a list of installed packages in the old IDE, and restore them in the new one (or copy them to another IDE).
However, if I remember correctly, these buttons do not support the list from the "Online Package Manager".