Mail is stored in a MYSQL db and attachments are stored in the filesystem when you are using Zarafa.
I've used the following procedure to backup mail and attachments on a server and restore it on another server.
Commands have to be performed with sudo or after sudo su
Backup
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STOP ZARAFA-SERVER
service zarafa-server stop
MAKE COPY OF EXISTING ATTACHMENTS
cd /var/lib/zarafa
tar -cvzf /var/tmp/attachments.tgz ./
FIND DATABASE PASSWORD
cat /var/lib/zentyal/conf/ebox-zarafa.passwd
DUMP MYSQL DATABASE
mysqldump -u zarafa -p -v --single-transaction zarafa > /var/tmp/zarafadump.sql
In /var/tmp/ you've got the files attachments.tgz and zarafadump.sql to backup or move to another server.
Restore
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STOP ZARAFA-SERVER
service zarafa-server stop
IMPORT ATTACHMENTS
mv /var/lib/zarafa /var/lib/zarafaOLD
mkdir /var/lib/zarafa
cd /var/lib/zarafa
tar -zxvf /var/tmp/attachments.tgz
chown root:root -R /var/lib/zarafa
cd /var/lib/zarafa
find . -type d -print0 | xargs -0 chmod 0700 # for directories
find . -type f -print0 | xargs -0 chmod 0644 # for files
FIND DATABASE PASSWORD
cat /var/lib/zentyal/conf/ebox-zarafa.passwd
IMPORT MYSQLDUMP (this may take a while depending on the size of your DB)
mysql -u zarafa -p zarafa < /var/tmp/zarafadump.sql
RESTART ZARAFA-SERVER
service zarafa-server start
TOOLS TO REATTACH MISSING STORES
zarafa-admin --list-orphans
zarafa-admin --hook-store STOREGUID -u username
zarafa-admin --remove-store STOREGUID