Yes you can migrate server and all the configurations.
Let's say we have two servers: Server1 (non AWS marketplace) and Server2 (AWS Marketplace instance).
Roughly you have to migrate folder /usr/local/FlashphonerWebCallServer from Server1 to Server2 with some tricks.
0. Stop WCS server on both servers.
sudo systemctl stop webcallserver
1. Backup the folder on Server2.
Make sure your backup is consistent.
Note. /usr/local/FlashphonerWebCallServer is a symlink. So you have to backup a real folder under this symlink.
2. Copy all the folder content from Server1 to Server2.
3. Copy early backed up file /usr/local/FlashphonerWebCallServer/conf/flashphoner.license from the backup to Server2.
4. Edit config /usr/local/FlashphonerWebCallServer/conf/flashphoner.properties and set:
ip = {Public IP AWS}
ip_local = {Private IP AWS}
5. Start WCS server.
sudo systemctl start webcallserver
It should be enough to migrate.
If something is going wrong, you can restore backup folder or launch AWS Marketplace image from a snapshot.