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If you have mapped volumes (I hope you do^^) you can either create the containers the same 8with same paths) in portainer or as other suggest it use docker-compose file/syntax for it. But keep in mind that when you rely on portainer, then keep backup of your configs.
As more advanced user I can tell you, that I use docker, docker-compose, docker swarm from cli and have portainer "only for the quick look". But this depends if you are cool with CLI or want to use a UI.
Portainer stores its own version of compose files in a specific place. I believe you can just copy your compose files into that place.
I would imagine you would have to rebuild them in portainer.
The good news is that portainer allows you to deploy either standalone containers or use docker-compose (portainer calls it stacks). So if you spin up said containers again and they have data paths that you can replicate, you should be able to just move your data over to the correct path on the new container that you have created
(random) Example: docker run -d -p 80:80 -v /some/path/to/content --restart unless-stopped somecompany/someapp:latest
If you were migrating that app you would need to just put the data back into the proper place (/some/path/to/content) for the container to recognize it. It would take some careful file transfers but it is DEFINITELY possible.
The bad news is that I dont know or understand the nature of your containers so im not sure what is needed specifically or where the containers were sourced/compiled from. Databases can be a bit trickier because they can be standalone dbs or they can be deployed with docker-compose alongside other containers as a service. You are going to have to work that bit out.