Migrate an unprivileged LXC container between users

I have an Ubuntu 14.04 server installation which acts as an LXC host. It has two users: user1 and user2. user1 owns an unprivileged LXC container, which uses a directory (inside /home/user1/.local/...) as backing store. How do I make a full copy of the container for user2? I can't just copy the files because they are mapped with owners ranging from 100000 to 100000+something, which are bound to user1. Also, which I believe is basically the same question, how can I safely make a backup of my user1's LXC container to restore it later on another machine and/or user?