There is no way to get anything installed in the container without modifying the container.
There are two ways to do this:
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build it into the image (the more correct approach)
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install it after the container is created and started
Building a new image is simple. In the docker file just base it on the official openHAB Image and add the necessary apt update and apt install ffmpeg commands to build the new image.
For option 2, you can just enter the container using docker exec -it openhab bash and run the apt commands manually. Of course you’ll have to redo this every time you change the container.
Alternatively you can mount a script that runs every time the container starts and have that run the apt commands. The down side of that is that it will run that every time the container starts, making it take longer for OH to come online. See the executing shell scripts before openHAB starts section of the docs on DockerHub.