rustybird I HAVE SUCCEEDED! Thank you all!
The solution was very very easy. I first opened the sms app, then the banking app. Put in my password. AND NOW: to get access to sms, swipe from the bottom of the screen, a small distance up and there you find all open apps. There you can go to sms and to get back to the banking app, do the same. The banking app then still is available!
Thank you all! It costed me 4 days and a lot of frustration...