Substitua isto:
50 5 * * * /home/user/bin/sync-folder
Com isso:
50 5 * * * /home/user/bin/sync-folder > /dev/null 2>&1
Adicione um email dentro do script:
#!/bin/bash
sudo rsync -rav --delete --log-file=/tmp/rsync-output /origin /destination
grep folder /tmp/rsync-output
if [ $? == 0 ]; then
mailx -s "Rsync Complete at 'date +"%F %T"'" [email protected] < /tmp/rsync-output
fi