Use the Sign-in Micro flow. This will make it possible to bring an object from the anonymous session into the logged in session. In the sign in microflow, just associate the object to your account object.
In the navigation you have to check if the object is connected if you want to show a specific page instead of the users landing page.
Here is some more info on how to achieve this:
project, security use the sign in microflow option for anonymous users
I would try to use the Deeplink module from the App Store to open the Request object created anonymously - you can use any unique value on the request object as the parameter for the deeplink microflow. If the Deeplink microflow has permissions other than anonymous, then the user will be prompted to login when accessing the deeplink.