We are currently using Google Apps for Business with 10 users, however yesterday a member managed to delete all their emails.
Is there any free option in order to backup all emails?
There is a Google Apps Admin Command line tool that allows extended admin provisions: Google Apps Manager
This tool can be used to download email held within accounts into MBOX format
I recommend Google Vault however.
Yes, there is Google Apps Mail Backup toolkit which is user friendly and all in one. Download and try demo, it supports all Windows and supports multiple mail account. It works well and save mailbox data in PST, MSG, MBOX and EML.
If they did this within the past 25 days you can try the native G Suite restore option.
You specified free, but FYI some great paid options are Spanning, Backupify, and SysCloud