mvBackup.sh

#!/bin/bash

# Test if file exists
backups=$(ls -1 $1/|wc -l)
if [ $backups -gt 0 ]
then
  rsync -a --remove-source-files --chown=defaultuser:defaultuser $1/ $2
else
  exit
fi

# Count amount backup
files=$(ls -1 $2| wc -l)

# Keep only two latest backup
if [ $files -gt 2 ]
then
  cd $2
  rm $(ls -1t $2| sed -n '3,$p')
fi

How to use it:

./mvBackup.sh /directory/where/backup/are/saved /where/to/move/backup