Posted by Quota is one of many attribute that should be migrated while doing migrating from old to the new Zimbra. First, you should export value of quota on the old Zimbra and second, you should import the result of export to the new Zimbra. The following is what i do for export/import quota from old to the new Zimbra.
On the old Zimbra Mail Server
# Create simple script for retrieve information of quota
1.chmod 775 /srv/2.chgrp zimbra /srv/3.vi /srv/getquota.shFill with the following line
01.#!/bin/bash02.rm /srv/modify-quota.zmp03.touch /srv/modify-quota.zmp04. 05.echo "Process Export Quota"06.zmprov -l gaa | while read ACCOUNT07.do08.QUOTA_TOTAL=`zmprov ga ${ACCOUNT} | grep "zimbraMailQuota" | cut -d ":" -f2`09.echo "ma ${ACCOUNT} zimbraMailQuota${QUOTA_TOTAL}"10.done >> /srv/modify-quota.zmp# Save and execute the script
1.chmod +x /srv/getquota.sh2.su - zimbra3.sh /srv/getquota.shThe results of above script is file with name modify-quota.zmp that saved in folder /srv/. Copy the file to the new Zimbra mail server
On the new Zimbra Mail Server
Assuming the file modify-quota.zmp is placed in /srv/ folder. Run the following command as Zimbra user
1.su - zimbra2.zmprov < /srv/modify-quota.zmpPlease check one of accounts whether value of quota has been changed or not. If you having trouble, please feel free to contact me on the comment form 
Good luck and hopefully useful
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