Hello Stijn,
What you can do is create an entity ‘Notification’ (attached to Account/User) that gets filled whenever you want it. So in your case for example when the quotation is accepted for a specific user, you create a new notification object and connect it to the right user.
Then after the login from you check (retrieve) whether there is a notification for this specific user and if so, you show one with a pop-up.
Good luck!
Cheers,
Mark