Is there a way to keep an old Android installation as virtual machine? With PCs I have made good experiences virtualizing the machine when changing to a new system (e.g., buy a new computer, change the operation system). Doing this, you can preserve your old system and restart it virtually if you would like to look up anything about your old system (e.g., a settings within a software tool).

As I have an issue with my not so old smartphone now and probably have to hand it in for repair, I would like to do the same with my Android system. I already did a backup using adb.exe from Android-SDK. Now, I am wondering if these backup-files represent a proper image and if there is a way to initiate these images in a virtual machine!? 

On the web I could not find any solution. There are lots of instructions of how to run Android-x86 as virtual machine. But that is not exactly what I am looking for.
ADB backs up Settings + Apps(System + User) + Apps Data + User Data. That's it. The backup made through it doesn't come close to be related to booting it into virtual machine or even a real device. Short story, you have a backup definitely but that's not a system image.

If you want to create a system image, you need to do it through a Nandroid backup or a custom tool. For the former, you require a custom recovery installed. But even that backup cannot be virtualized on a PC, not that I'm aware of any of yet.

However, you can virtualize (running real actually) this Nandroid backup using MultiRom. I did not use MultiRom but I found that folks use it to boot multiple Android OS. I'm yet to be certain whether this backup can be installed in a seconday ROM, I suppose it should be.
Besides, the last time I checked for Android virtualization, I got Android 4.3 as the latest available iso when 5.0 for devices was already launched. 

Note: This is an attempt and is far away from a good answer. Nonetheless, it doesn't qualify to be a comment either.