1) Stop the container (you can do it from the proxmox web interface but considering that you will need ssh access to the server the complete the other steps, I have stopped the container using a simple command issued on the linux shell prompt):
pct stop container-id

2) Create a full container backup (to preserve the actual information within the container):
vzdump container-id -storage local -compress lzo

3) Destroy the container
pct destroy container-id

4) Restore the container from the previous created backup
pct restore container-id /var/lib/vz/dump/vzdump-lxc-container-id-2017_02_13-16_50_29.tar.lzo --rootfs local-lvm:25

Some infos about step 4:
The default backup location is /var/lib/vz/dump
When you create a backup using vzdump the file structure for the backup is: vzdump-lxc-container-id–year_month_day–hour_minutes_seconds.tar.lzo
local-lvm represents the name (description) of the local storage volume as shown in the proxmox web interface (Storage View); depending of your configuration, the name is probably different