Say you have a smartphone with two browsers, DefaultBrowser and OtherBrowser.  
- You visit the webshop by opening 
Otherbrowser, and proceed through the cart steps - At the end, you go from 
OtherBrowsertoPaymentAppto pay. - After you've paid, 
PaymentAppcloses and opens the confirmation URL in theDefaultBrowser. 
And that last step is a problem. DefaultBrowser doesn't have the right session, OtherBrowser does.
The PaymentApp does as expected, it opens a browser instance and the OS picks the set default.
I strongly prefer not to set a new session in DefaultBrowser based and feedback parameters (like order_id) as I want to keep it as secure and transparent as possible. Extra downside of this is that the real session is still alive in OtherBrowser which might lead to other problems or confusion.
Does anyone have a solution for this? I'm not perse looking for some code, instead im looking for a concept which could fix it as good as possible.
Some additional information:
- We do not own the app. I can contact them, but it's a bank app and I'm a mere peasant.
 - Other big webshops have the exact same situation.
 - This is not brand related, Android/iOS (and likely WinPhone) have this problem.
 - This is not app related, we tried a few bank apps, all have this exact problem.