@Franko999 Apologies for the delay.
Container can be moved from one box to another basis several parameter. Storing files in container is not the right approach as they can be moved (and hence data is lost) from them.
In order to have persistence storage, you will need to mount the volume to container (which is backed by azure file system). Read more about it from Persistence Volume section.
Above solution is assuming you are using azure container services (ACS). There is similar solution if you are using AKS (azure Kubernetes solution). In case of AKS, you will need to create persistence volume claim and use it to store persistent data.
In case you are using AKS, let me know and I will share the exact documentation to do the same.